Birational Geometry of Hypersurfaces
Gargnano del Garda, Italy, 2018
Seiten
2019
|
1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-18637-1 (ISBN)
Springer International Publishing (Verlag)
978-3-030-18637-1 (ISBN)
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.
- 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-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.
| Erscheinungsdatum | 19.10.2019 |
|---|---|
| Reihe/Serie | Lecture Notes of the Unione Matematica Italiana |
| Zusatzinfo | IX, 297 p. 36 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 474 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | 14-06,14E08,16E35,14D22,14C30 • Algebraic Geometry • cubic fourfolds • derived categories • K3 surfaces • Rational Varieties |
| ISBN-10 | 3-030-18637-7 / 3030186377 |
| ISBN-13 | 978-3-030-18637-1 / 9783030186371 |
| Zustand | Neuware |
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