短期课程“Birational geometry of complex algebraic surfaces”

1. 主讲人：

陈伊凡

2. 时间和地点：

·       11月3日，9:00-11:00, 实验楼103

·       11月5日，8:00-10:00，实验楼103

·       11月6日，14:00-16:00, 实验楼110

3. 专家简介：

陈伊凡，北京航空航天大学数学科学学院副教授；2013年博士毕业于北京大学，期间曾到德国Bayreuth大学进行联合培养，并取得德国的博士学位。陈伊凡的研究领域是代数几何，研究内容涉及代数曲面及三维簇的分类问题，研究成果发表在 Mathematische Zeitschrift, Bulletin of the London Mathematical Society, Manuscripta Mathematica, Nagoya Mathematical Journal 等杂志。

4.    短课程摘要：

This short course gives an introduction to the birational geometry of complex algebraic surfaces, from the point of view of the minimal model program.

The first talk will briefly recall the intersection theory on surfaces, the Riemann-Roch theorem, the adjunction formula and Castelnuovo's contratibility criterion. Then we prove the extremal contraction theorem for a surface S with K_S non-nef, via the rationality theorem and the base-point-freeness theorem.

The second talk will deal with the cone theorem and the contraction theorem. Then we show that the minimal model program for surfaces yields either a Mori fiber space or a minimal model. We also talk about the basic properties of a Mori fiber space.

The third talk will introduce the basic properties of a minimal model: nonnegativity of the Euler characteristic, nonvanishing and abundance.