Facets of Algebraic Geometry: Volume 1

Paolo Aluffi is Professor of Mathematics at Florida State University. He earned a Ph.D. from Brown University with a dissertation on the enumerative geometry of cubic plane curves, under the supervision of William Fulton. His research interests are in algebraic geometry, particularly intersection theory and its application to the theory of singularities and connections with theoretical physics. David Anderson is Associate Professor of Mathematics at The Ohio State University. He earned his Ph.D. from the University of Michigan, under the supervision of William Fulton. His research interests are in combinatorics and algebraic geometry, with a focus on Schubert calculus and its applications. Milena Hering is Reader in the School of Mathematics at the University of Edinburgh. She earned a Ph.D. from the University of Michigan with a thesis on syzygies of toric varieties, under the supervision of William Fulton. Her research interests are in algebraic geometry, in particular toric varieties, Hilbert schemes, and connections to combinatorics and commutative algebra. Mircea Mustaţă is Professor of Mathematics at the University of Michigan, where he has been a colleague of William Fulton for over 15 years. He received his Ph.D. from the University of California, Berkeley under the supervision of David Eisenbud. His work is in algebraic geometry, with a focus on the study of singularities of algebraic varieties. Sam Payne is Professor in the Department of Mathematics at the University of Texas at Austin. He earned his Ph.D. at the University of Michigan, with a thesis on toric vector bundles, under the supervision of William Fulton. His research explores the geometry, topology, and combinatorics of algebraic varieties and their moduli spaces, often through relations to tropical and nonarchimedean analytic geometry.

• 1. Positivity of Segre–MacPherson classes Paolo Aluffi, Leonardo C. Mihalcea, Jörg Schürmann and Changjian Su; 2. Brill–Noether special cubic fourfolds of discriminant 14 Asher Auel; 3. Automorphism groups of almost homogeneous varieties Michel Brion; 4. Topology of moduli spaces of tropical curves with marked points Melody Chan, Søren Galatius and Sam Payne; 5. Mirror symmetry and smoothing Gorenstein toric affine 3-folds Alessio Corti, Matej Filip and Andrea Petracci; 6. Vertex algebras of CohFT-type Chiara Damiolini, Angela Gibney and Nicola Tarasca; 7. The cone theorem and the vanishing of Chow cohomology Dan Edidin and Ryan Richey; 8. Cayley–Bacharach theorems with excess vanishing Lawrence Ein and Robert Lazarsfeld; 9. Effective divisors on Hurwitz spaces Gavril Farkas; 10. Chow quotients of Grassmannians by diagonal subtori Noah Giansiracusa and Xian Wu; 11. Quantum Kirwan for quantum K-theory E. González and C. Woodward; 12. Toric varieties and a generalization of the Springer resolution William Graham; 13. Toric surfaces, linear and quantum codes – secret sharing and decoding Johan P. Hansen.