Lectures On K3 Surfaces

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Lectures on K3 Surfaces

Author: Daniel Huybrechts
language: en
Publisher: Cambridge University Press
Release Date: 2016-09-26
Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.
Birational Geometry of Hypersurfaces

Author: Andreas Hochenegger
language: en
Publisher: Springer Nature
Release Date: 2019-10-08
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.
Lectures on Logarithmic Algebraic Geometry

Author: Arthur Ogus
language: en
Publisher: Cambridge University Press
Release Date: 2018-11-08
A self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.