课程题目：Complex Curves and Surfaces
授课人：Cristiano Spotti (Institut des Hautes Études Scientifiques)
The focus of the lectures will be on "classificatory aspects" in low dimensional complex geometry, using both analytic/differential and algebro geometric techniques.
The course will be roughly divided into three parts:
Part 1, Overview of the Foundation of Complex Geometry: Complex, Kahler, Algebraic manifolds (definitions, examples); Line bundles (divisors), Sheaves & Cohomology.
Part 2, Compact Complex Curves: Basic theorems, e.g. algebricity, Riemann-Roch; Uniformization Theorem (proof of the existence of a constant curvature metric);
Examples and constructions of Moduli Spaces, e.g. (Hyper)elliptic curves.
Part 3, Compact Complex Surfaces. Basic techniques. Examples. Birational Geometry of algebraic surfaces. Enriques-Kodaira birational classification of algebraic surfaces using Mori's Minimal-Model-Program framework.
Prerequisites: Functions of Complex Variables, Foundations of Differential Geometry. At some point some familiarity with (co)homology theories and some basic PDE may be helpful but not strictly necessary.
Cristiano Spotti 概况：
Cristiano Spotti, a wonderful talented young differential geometer who is a former student of Sir Simon Donaldson. His recent work with S. Sun and Odoka on moduli space of Fano surface is a fundamental work in Kaehler geometry. Among other things they proved,in particular, they also give a new, uniformed treatment to the well known theorem of Tian on the resolution of the Calabi conjecture in Fano surface. He is currently at IHES, France. His lecture is crystal clear.