Birational Geometry, Rational Curves, and Arithmetic

F. Bogomolov is Professor at the Courant Institute, NYU. He is best known for his pioneering work on hyperkähler manifolds. B. Hassett is Professor and Chair of the department of Mathematics at Rice University. He published two books and around 50 papers on Algebraic and Arithmetic Geometry. Yuri Tschinkel is Professor at the Courant Institute, NYU and Director of the Mathematics and the Physical Sciences Division at the Simons Foundation.

• ​​Foreword.- Introduction.- A. Bertram and I. Coskun, The birational geometry of the Hilbert scheme of points on surfaces.- F. Bogomolov and Ch. Böhning, Isoclinism and stable cohomology of wreath products.- F. Bogomolov, I. Karzhemanov, and K. Kuyumzhiyan, Unirationality and existence of infinitely transitive models.- I. Cheltsov, L. Katzarkov, and V. Przyjalkowski, Birational geometry via moduli spaces.- O. Debarre, Curves of low degrees on projective varieties.- S. Kebekus, Uniruledness criteria and applications.- S. Kovács, The cone of curves of K3 surfaces revisited.- V. Lazić, Around and beyond the canonical class.- C. Liedtke, Algebraic surfaces in positive characteristic.- A. Varilly-Alvarado, Arithmetic of Del Pezzo surfaces.​