Birational Geometry of Hypersurfaces: Gargnano del Garda, Italy, 2018

by Andreas Hochenegger, Manfred Lehn, Paolo Stellari

Overview

Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results.

The aim of the school was to shed light on this vast area of research by concentrating on two main aspects: (1) Approaches focusing on (stable) rationality using deformation theory and Chow-theoretic tools like decomposition of the diagonal; (2) The connection between K3 surfaces, hyperkähler geometry and cubic fourfolds, which has both a Hodge-theoretic and a homological side.

Featuring the beautiful lectures given at the school by Jean-Louis Colliot-Thélène, Daniel Huybrechts, Emanuele Macrì, and Claire Voisin, the volume also includes additional notes by János Kollár and an appendix by Andreas Hochenegger.

Product Details

ISBN-13:	9783030186371
Publisher:	Springer International Publishing
Publication date:	10/09/2019
Series:	Lecture Notes of the Unione Matematica Italiana , #26
Edition description:	1st ed. 2019
Pages:	297
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

- Part I Birational Invariants and (Stable) Rationality. - Birational Invariants and Decomposition of the Diagonal. - Non rationalité stable sur les corps quelconques. - Introduction to work of Hassett-Pirutka-Tschinkel and Schreieder. - Part II Hypersurfaces. - The Rigidity Theorem of Fano–Segre–Iskovskikh–Manin–Pukhlikov–Corti–Cheltsov–deFernex–Ein–Mustaţă–Zhuang. - Hodge Theory of Cubic Fourfolds, Their Fano Varieties, and Associated K3 Categories. - Lectures on Non-commutative K3 Surfaces, Bridgeland Stability, and Moduli Spaces. - Appendix: Introduction to Derived Categories of Coherent Sheaves.