数学科学院几何学 Seminar 系列讲座之三十七

题  目：Introduction to Algebraic Deformation Theory

报告人：许金兴(USTC)

时  间：10月25日, 11月1, 8, 15日 下午2:30-4:30 (共四次)

地  点：管理科研楼 1318

摘  要：Deformation theory is a useful tool in the local study of moduli spaces.  The deformation theory of complex manifolds was studied by K. Kodaira and D.C. Spencer, and their theory was adopted by A. Grothendieck to abstract algebraic geometry. I will give an introduction to deformation theory in algebraic geometry. Topics will include:

 1. Deformation theory as the infinitesimal study of moduli spaces
 2. Tangent spaces and obstruction theories
 3. From formal deformations to actual deformations: Grothendieck's existence theorem and M. Artin's approximation theorem  
 4. Typical examples: deformations of varieties, closed subvarieties and vector bundles
 5. Hilbert schemes and moduli space of stable curves

主办单位：中国科大数学科学学院    国家数学与交叉科学中心合肥分中心

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