Birational Geometry, Rational Curves, and Arithmetic

• Corporate Author: SpringerLink (Online service)
• Other Authors: Bogomolov, Fedor (Editor), Hassett, Brendan (Editor), Tschinkel, Yuri (Editor)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2013.
• Subjects: Mathematics.; Algebraic geometry.; Geometry.; Number theory.; Algebraic Geometry.; Number Theory.

This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry.  It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions.  Classically, arithmetic is the stu...

Table of Contents:

• 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.