Title of the course: Deformations of Fano and Calabi-Yau Varieties
Instructor: Dr. Taro Sano
Institution: Kobe University
Dates: 27 January – 2 February 2020
Prerequisites: Basic complex algebraic geometry (not a must but preferable)
Level: Graduate Advanced undergraduate
Abstract: In this lecture series we present an algebraic approach to deformations of Fano and Calabi-Yau varieties. Fano varieties and Calabi-Yau varieties are important objects in the classification of algebraic varieties. In the classification of vareties, it is fundamental to study their deformations. Starting from basic notions, I’ll explain how to see that they have unobstructed deformations. I’ll also explain the generalization to log CY varieties and normal crossing CY varieties. Daily description is as follows.
1: Basics on complex manifolds (analytic spaces) and sheaves
2: Preliminaries on Deformation theory
3: Deformations of CY varieties (Bogomolov-Tian-Todorov theorem)
4: Deformations of log CY and normal crossing CY varieties
Textbook and References:
1. Greuel, G.-M.; Lossen, C.; Shustin, E. Introduction to singularities and deformations. Springer Monographs in Mathematics. Springer, Berlin, 2007. xii+471 pp.
2. Huybrechts, Complex geometry, An introduction. Universitext. Springer-Verlag, Berlin, 2005. xii+309 pp.
3.Namikawa, Yoshinori Calabi-Yau threefolds and deformation theory [translation of Sūgaku 48 (1996), no. 4, 337–357; MR1614448]. Suguku Expositions. Sugaku Expositions 15 (2002), no. 1, 1–29.
4. Sernesi, Edoardo Deformations of algebraic schemes. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 334. Springer-Verlag, Berlin, 2006. xii+339 pp.
Language: EN