Birational geometry of hypersurfaces : Gargnano del Garda, Italy, 2018
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Bibliographic Information
Birational geometry of hypersurfaces : Gargnano del Garda, Italy, 2018
（Lecture notes of the Unione matematica italiana, 26）
Springer, c2019
Available at 8 libraries
Note
Contributions in English and French
"This volume originates from the 'School on Birational Geometry of Hypersurfaces,' which took place in the Palazzo Feltrinelli in Gargnano del Garda in March 2018"--Pref
Includes bibliographical references
Description and Table of Contents
Description
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, hyperkahler 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-Thelene, Daniel Huybrechts, Emanuele Macri, and Claire Voisin, the volume also includes additional notes by Janos Kollar and an appendix by Andreas Hochenegger.
Table of Contents
- Part I Birational Invariants and (Stable) Rationality. - Birational Invariants and Decomposition of the Diagonal. - Non rationalite 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-Mustata-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.
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