ZAG Handbook of Algebraic Geometry

Ivan Cheltsov is Professor at the University of Edinburgh, and his research interests include birational geometry and K-stability of Fano varieties. He is author of 3 books and 126 papers written together with 52 co-authors. Ivan has organized research meetings in Auckland, Beijing, Cambridge, Durham, Edinburgh, Fuerteventura, Istanbul, Levico Terme, London, Magadan, Melbourne, Moscow, New York, Oberwolfach, Pipa, Pohang, Easter Island, Shanghai, Sochi, Spitsbergen, Stony Brook, Sydney, Tianjin, Wakkanai, Vladivostok. Since 1995, Ivan is married to Elena Cheltsova: they have three children (Ivan, Fedor, Ekaterina) and cat Kuzya. Aside of Mathematics, Ivan enjoys traveling, reading and cycling his Brompton bicycle. Jesus Martinez-Garcia is Senior Lecturer in Pure Mathematics at the University of Essex (UK). He obtained his PhD at the University of Edinburgh in 2013 and has held research positions at the University of Bath (UK), Johns Hopkins University (US) and the Max Planck Institute for Mathematics (Germany). His research is in algebraic geometry with special emphasis on birational geometry, moduli spaces, K-stability, Fano varieties and computational algebraic geometry. Martinez-Garcia has written one book, several research articles and two software packages and he has co-organised more than 10 research meetings, including the annual international conference AGGITatE as well as several research seminars.

• Table of Contents1. Algebraic geometry in the times of CovidIvan Cheltsov and Jesus Martinez-Garcia2. Models of Fano 3-foldsHamid Abban3. Weighted Ehrhart polynomials and series for the standard simplexPraise Adeyemo4. Advances in moduli theoryJarod Alper5. Normal form of a holomorphic Lagrangian submanifoldEkaterina Amerik6. Koszul modules and applicationsMarian Aprodu7. Euler characteristics of aspherical Kähler manifoldsDonu Arapura8. Birational geometry of Calabi-Yau pairs and Cremona transformationsCarolina Araujo9. Enumerating punctured log maps via wall-crossingHulya Arguz10. Biregular and birational geometry of rational nodal quartic double solidsArtem Avilov11. Chern character of quantizable sheavesVladimir Baranovsky and Victor Ginzburg12. Vector bundles on Fano threefolds and K3 surfacesArnaud Beauville13. Cylinders in Del Pezzo surfaces with Du Val singularitiesGrigory Belousov14. Approximation of differentiable submanifolds by real algebraic subvarietiesOlivier Benoist15. Kähler-Einstein metrics, Archimedean zeta functions and phase transitionsRobert Berman16. Geometry of 3-dimensional Del Pezzo fibrations in positive characteristicFabio Bernasconi17. Geometry of polarised varietiesCaucher Birkar18. On properness of K-moduli spaces and optimal destabilizationsHarold Blum19. Surface with ample canonical bundle and Kuranishi space a nonreduced pointChristian Boehning20. Projective geometry approach to the Jacobian conjectureAlexander Borisov21. Explicit equations of surfaces of general typeLev Borisov22. General type results for moduli of hyperkähler varietiesEmma Brakkee23. Geometric structures on spaces of quadratic differentialsTom Bridgeland24. Extending Tom and Jerry for Fano 3-foldsGavin Brown, Stephen Coughlan and Tom Ducat25. Supercycles and stable supermapsUgo Bruzzo and Daniel Hernandez Ruiperez26. Arcs and singularitiesNero Budur27. Chern–Weil theory and Hilbert–Samuel theorem for semipositive singular toroidal metricsJose Ignacio Burgos Gil28. Index 2 Fano 3-folds and double coversLivia Campo29. Uniqueness of enhancements of triangulated categoriesAlberto Canonaco, Amnon Neeman and Paolo Stellari30. On the birational geometry of foliationsPaolo Cascini31. Effective cones of moduli spaces of stable rational curves and blown up toric surfaces Ana-Maria Castravet32. Nodal surfaces, coding theory, and cubic discriminantsFabrizio Catanese33. The minimal model program for arithmetic surfaces enriched by a Brauer classDaniel Chan34. Low dimensional components in the K-moduli of smoothable Fano 3-folds Ivan Cheltsov35. Remarks on n-folds of type (1,n)Jungkai Chen36. Singularities on toric fibrationsYifei Chen and Caucher Birkar37. On the distribution of canonical volumes and moduli spaces of varieties of general typeMeng Chen38. Subadditivity theorem for Okounkov bodiesSung Rak Choi39. Enumeration of Terracini schemesCiro Ciliberto40. Numerical characterization of complex torus quotientsBenoit Claudon41. Slope inequalities and ample cone of KSB moduli spacesGiulio Codogni42. The cohomology of the moduli space of sheaves on surfacesIzzet Coskun43. Orbifold quot schemes via the le Bruyn–Procesi theoremAlastair Craw44. On quadratic points on intersections of two quadricsBrendan Creutz and Bianca Viray45. Deformations of exterior differential ideals and applicationsFernando Cukierman46. Log minimal model program for Kähler 3-foldsOmprokash Das47. CSCK metrics on rank one spherical Fano fourfoldsThibaut Delcroix48. K-stability of P^3 blown up along the disjoint union of a twisted cubic curve and a lineElena Denisova49. Stability of fibrationsRuadhai Dervan50. Wall crossing for K-moduli spaces of plane curvesKristin DeVleming51. The bottleneck degree of algebraic varietiesSandra Di Rocco52. Dynamical filtrations|Tien-Cuong Dinh, Hsueh-Yung Lin, Keiji Oguiso and De-Qi Zhang53. Roth's theorem for adelic curvesPaolo Dolce and Francesco Zucconi54. Enumerative geometry, fredholm analysis and moduli spaces of surfaces of general type Simon Donaldson55. Bounding the complexity of 2-loop Feynman integralsCharles Doran56. K-stability of P^3 blown up along smooth curves of genus 4 and degree 6Tiago Duarte Guerreiro57. Rigidity of affine Brieskorn-Pham threefoldsAdrien Dubouloz58. Birational geometry and cylindricity of Severi-Brauer varietiesAdrien Dubouloz, Kento Fujita, Takashi Kishimoto and Takuzo Okada59. Okawa's theorem and wide subcategories of coherent sheaves on curvesAlexey Elagin60. Mixed Hodge structure decomposition of alexander modules into generalized eigenspacesEva Elduque61. Local stability threshold of Del Pezzo surfaces of degree 2Erroxe Etxabarri Alberdi62. Rational simple connectedness and the quintic Del Pezzo threefoldAndrea Fanelli63. K3 structures from singular Fano varietiesEnrico Fatighenti64. An overview of homotopy path algebrasDavid Favero65. Quasi-invariants and free arrangementsMisha Feigin66. The Brasselet-Schurmann-Yokura conjecture on L-classes of singular varietiesJavier Fernandez de Bobadilla and Irma Pallares Torres67. Notes on motivic integration on Berkovich spacesTommaso de Fernex68. Counting sheaves by counting curvesSoheyla Feyzbakhsh and Richard Thomas69. On the boundedness of elliptically fibered Calabi-Yau threefoldsStefano Filipazzi70. Connected algebraic groups acting on Fano fibrations over P^1Enrica Floris71. Maximal automorphism groups of surfacesPascal Fong and Matilde Maccan72. A canonical Hodge theoretic projective structure on compact Riemann surfacesPaola Frediani73. On extremal contractions of log canonical pairsOsamu Fujino74. On the singular loci of higher secant varieties of Veronese embeddingsKatsuhisa Furukawa75. The Bourbaki degree of a plane curveDaniel Futata and Marcos Jardim76. Compactifications of the moduli space of marked cubic surfacesPatricio Gallardo77. Intrinsic mirrors for minimal adjoint orbitsElizabeth Gasparim78. On a generalized Batyrev’s cone conjectureYoshinori Gongyo79. Complex curves in hypercomplex nilmanifoldsIulia Gorginian80. Projective flatness over Klt spaces and characterisation of finite quotients of projective spacesDaniel Greb81. Distinguishing triangle-free level-one phylogenetic networks using computational algebraic geometryElizabeth Gross82. Open FJRW theory and mirror symmetry: a ZAG lectureMark Gross, Tyler Kelly and Ran Tessler83. Recent progress in the MMP for 3-folds and 4-folds in char p>0Christopher Hacon84. Rationality questions on Seshadri constantsKrishna Hanumanthu85. Log symplectic pairs and mixed Hodge structuresAndrew Harder86. Gaps between lc pairs and Klt pairs in a viewpoint of the minimal model theoryKenta Hashizume87. Constructing new Q-Fano threefolds using Laurent inversionLiana Heuberger88. Fano manifolds such that the tangent bundle is (not) bigAndreas Hoering89. Geometric extensionChris Hone and Geordie Williamson90. An algebro-geometric higher Szemeredi lemmaEhud Hrushovski91. A dynamical approach to generalized Weil's Riemann hypothesis and semisimplicity Fei Hu92. Torelli problem on logarithmic sheavesSukmoon Huh93. Minimal rational curves and 1-flat cone structuresJun-Muk Hwang94. A bound of the number of weighted blow-ups to compute the minimal log discrepancy for smooth 3-folds Shihoko Ishii95. The McKay correspondenceYukari Ito96. Shafarevich's conjecture for canonically polarized varieties revisitedAriyan Javanpeykar, Steven Lu, Ruiran Sun and Kang Zuo97. Symmetries of Fano varietiesLena Ji98. Minimal log discrepancies in dimension threeChen Jiang99. Equilateral convex triangulations of RP^2 with three conical points of equal defecNikita Kalinin100. 1-dimensional K-moduli spaces of Fano 3-foldsAnne-Sophie Kaloghiros101. A brief survey on stability of tangent bundles on Fano manifoldsAkihiro Kanemitsu102. Are Klt Fano varieties of small volume stably rational?Ilya Karzhemanov103. New examples of surgery invariant counts in real algebraic geometrySlava Kharlamov104. Hodge sheaves for singular familiesSandor Kovacs105. Secant varieties of real curvesMario Kummer106. Sextic double solidsAlexandra Kuznetsova107. On effective cones of rational surfacesAntonio Laface108. The rational chow rings of M_7, M_8 and M_9Hannah Larson109. A Néron-Ogg-Shafarevich criterion for K3 surfacesChris Lazda110. Derived categories and motives of moduli spaces of vector bundles on curvesKyoung-Seog Lee111. Dominant rational maps from a very general hypersurfaceYongnam Lee112. Valuative stability of polarised varietiesEveline Legendre113. Rational curves on Del Pezzo surfaces in positive characteristicBrian Lehmann114. Codimension 2 cycles of classifying spaces of low-dimensional algebraic toriNicole Lemire115. Locally free twisted sheaves of infinite rankMax Lieblich116. Rational curves on K3 surfacesChristian Liedtke117. Automorphisms of projective hypersurfacesAlvaro Liendo118. Motivic invariants of birational maps Hsueh-Yung LinEvgeny Shinder119. A motivic version of topological mirror symmetryFransois Loeser120. Poisson and symplectic geometry of the moduli spaces of Higgs bundlesMarina Logares121. On non-rationality of degenerations of Del Pezzo surfacesKonstantin Loginov122. A conjecture on D algebrasLeonid Makar-Limanov123. Fano threefolds of Picard rank 2 and volume 28Joseph Malbon124. Birational involutions of the real projective plane fixing an irrational curveFrederic Mangolte125. Unirationality of instanton moduli space for small chargesDimitri Markushevich and Alexander Tikhomirov126. The defect of a cubic threefoldLisa Marquand127. The determinant of cohomology and moduli of lambda-connectionsJohan Martens128. Two remarks on asymptotically log Fano pairsJesus Martinez-Garcia129. On K-stability of Calabi-Yau fibrationsHattori Masafumi130. On the (uni)rationality problem for hypersurfacesAlex Massarenti131. Transformations of transfinite diameterSione Ma`u132. Perverse-Hodge octahedronMirko Mauri133. A special rational surfaceMassimiliano Mella134. On the top-weight rational cohomology of A_gMargarida Melo135. Jordan property for automorphism groupsSheng Meng136. Geometry and arithmetic of equivariant compactifications of the affine spacePedro Montero137. Special variational Hodge conjecture for toric varietiesWilliam Montoya138. Tropical geometry and phylogenetic diversityHan-Bom Moon139. Fundamental groups of singularities of the MMPJoaquin Moraga140. A moduli space in the differential geometry worldDavid Mumford141. Interview with David MumfordIvan Cheltsov and Jesus Martinez-Garcia142. The Kawamata–Viehweg vanishing theorem for schemesTakumi Murayama143. Minimal exponent and Hodge filtrationsMircea Mustata144. Inversion of adjunction for quotient singularitiesYusuke Nakamura145. On compatifying moduli and degenerations of K-trivial varietiesYuji Odaka146. K-stability and birational superrigidity for Fano 3-fold weighted hypersurfacesTakuzo Okada147. Moduli space of semiorthogonal decompositionsShinnosuke Okawa148. Stable irrationality of the very general quartic fivefoldJohn Christian Ottem149. Contact in algebraic and tropical geometryMarco Pacini and Damiano Testa150. Extended abstract of counting divisorial contractions with centre a cA_n-singularityErik Paemurru151. Fine compactified Jacobians of nodal curvesNicola Pagani152. On polynomial automorphisms commuting with a simple derivationIvan Pan153. K-moduli for log Fano complete intersectionsTheodoros Stylianos Papazachariou154. Cayley octads, plane quartic curves, Del Pezzo surfaces of degree 2, and double Veronese conesJihun Park155. A Castelnuovo-Mumford regularity bound for threefolds with rational singularitieJinhyung Park156. Moderately discontinuous algebraic topology and singularitiesMaria Pe Pereira157. Generic flexibility of cubic conesAlexander Perepechko158. Serre functors of semiorthogonal componentsAlex Perry159. Deformations of toric singularities and applications to K-moduli of Fano varietiesAndrea Petracci160. Campana points on Fano varietiesMarta Pieropan161. On canonical threefolds near the noether lineRoberto Pignatelli162. K-stability and space sextic curves of genus threeAntoine Pinardin163. On local-global principles and Galois cohomologyAlena Pirutka164. Conic-line arrangements in the complex projective planePiotr Pokora165. Hyperelliptic limits of quadrics through canonical curves and the super-Schottky locusAlexander Polishchuk166. General elephants for 3-fold extremal contractionsYuri Prokhorov167. Rationally connected rational double covers of primitive Fano varietiesAleksandr Pukhlikov168. Singularities and divisors in the moduli space of surfacesJulie Rana169. Sheaf counting of Hilbert schemes of points on C^4Jorgen Rennemo170. Wall-crossing pathologies in three dimensionsFatemeh Rezaee171. K-polystability of smooth Fano SL_2-threefoldsJack Rogers172. Hodge-Riemann classes and schur polynomialsJulius Ross173. The splendour of asymptotically log Del PezzosYanir Rubinstein174. Smoothing toroidal crossing Fano 3-foldsHelge Ruddat175. An overview on mordell–Weil rank jumps for fibers of elliptic surfacesCecilia Salgado176. Blow-ups with log canonical singularitiesGregory Sankaran177. On birational boundedness of some Calabi–Yau hypersurfacesTaro Sano178. Equivariant solidity of the three-dimensional projective spaceArman Sarikyan179. Near-rationality properties of norm varietiesAnand Sawant180. Generalized hyperpolygons and applicationsLaura Schaposnik181. Equality in the Bogomolov-Miyaoka-Yau inequality in the non-general type caseStefan Schreieder182. Rational curves on Enriques surfaces, but only fewMatthias Schuett183. Cohomology of the moduli of Higgs bundles and the Hausel-Thaddeus conjectureJunliang Shen184. Survey of the article on Atiyah class and sheaf counting on local Calabi-Yau fourfoldsArtan Sheshmani185. Automorphism groups of complex elliptic surfacesConstantin Shramov186. Lebrun-Salamon conjecture from the effective nonvanishing for Fano manifoldsRobert Smiech187. Partial order on involutive permutations and double Schubert cellsEvgeny Smirnov188. Geometric aspects of Kähler-Einstein metrics on Klt pairs: a remark on optimal Bogomolov-Miyaoka-Yau inequalityCristiano Spotti189. Weak Del Pezzo surfaces with global vector fieldsClaudia Stadlmayr190. Local volumes of singularities and the mahler conjecture for convex bodiesHendrik Suess191. Higher order minimal families of rational curves on Fano manifoldsTaku Suzuki192. An O-acyclic variety of even indexFumiaki Suzuki193. The Mukai model of M_7David Swinarski194. Local effectivity in projective spacesTomasz Szemberg195. Fermat type arrangements and the containment problemJustyna Szpond196. Birational properties of base spaces of smooth projective families of good minimal modelsBehrouz Taji197. Key varieties for prime Q-Fano threefolds of codimension 4Hiromichi Takagi198. Deformations of F-pure and F-regular singularitiesShunsuke Takagi199. On Mori fibre spaces in positive characteristicHiromu Tanaka200. Rational curves on Fano threefoldsSho Tanimoto201. Delta invariants of quasi-smooth hypersurfacesLuca Tasin202. Real structures on almost homogeneous varietiesRonan Terpereau203. Mirror symmetry for fibrations and degenerationsAlan Thompson204. On a logarithmic version of a theorem of EnriquesSofia Tirabassi205. Equivariant birational typesYuri Tschinkel206. Vector fields on canonically polarized surfacesNikos Tziolas207. Noncommutative Del Pezzo surfacesKazushi Ueda208. Exceptional collections on Σ_2Hokuto Uehara209. Counts of secant planes to varieties, degenerations, and universal polynomialsMara Ungureanu210. Actions of Cremona groups on CAT(0) cube complexesChristian Urech211. Artin-Mumford counterexample, with generalizations, via Enriques surfacesAlessandro Verra212. Higher Fano manifoldsNivedita Viswanathan213. Global Brill-Noether theory over the Hurwitz spaceIsabel Vogt214. Positivity of the second exterior power of the tangent bundlesKiwamu Watanabe215. Pinched handle decompositions of finite simplicial complexesJean-Yves Welschinger216. Concurrent exceptional curves on Del Pezzo surfaces of degree one and torsion points on elliptic fibrationsRosa Winter217. Rational maps via C^*-actionsJaroslaw Wisniewski218. On weighted Del Pezzo hypersurfacesJoonyeong Won219. Equivariant birational geometry of linear actionsKaiqi Yang220. Equivariant birational rigidity: around one question of Cheltsov and KollárEgor Yasinsky221. Stringy motives and local fundamental groups of Klt surface singularities in arbitrary characteristicTakehiko Yasuda222. Degenerations, fibrations and mirror symmetryFenglong You223. Stability of pencils of plane curvesAline Zanardini224. Jordan properties of automorphism groups of algebraic varieties and complex manifoldsYuri Zarhin225. Basis divisors and balanced metricsKewei Zhang226. The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefoldsZheng Zhang227. Equivariant geometry of singular cubic threefoldsZhijia Zhang228. Topological SYZ fibrations with discriminant in codimension 2Ilia Zharkov229. Compact Kähler threefolds with the action of an abelian group of maximal dynamical rankGuolei Zhong230. Equivariant K-stability under finite group actionZiwen Zhu231. K-stability of Fano varieties via admissible flagsZiquan Zhuang232. Unbounded connected algebraic subgroups of birational transformationsSokratis Zikas233. Finite quotients of Cremona groupsSusanna Zimmermann