时间：2021年12月21日-2022年1月15日 11:00-13:00

Time：11:00-13:00, December 21, 2021 - January 15, 2022

线上：腾讯会议ID：712-7482-4934, 密码：666666

Online: Tencent Meetings ID: 712-7482-4934, Password: 666666

本次短期课程将采取线上的方式举行，时间定于每周二和每周五的11:00-13:00

主讲嘉宾/Speaker：Prof. Wenbo Niu, University of Arkansas

短期课程名称/Title：Lectures on Syzygies of algebraic varieties II

介绍/Introduction:

This lecture is the continuation of the lecture given in 2019. However, it does not require the familiarity with the 2019 lecture. We consider a projective algebraic variety embedded in a projective space by a very ample line bundle. The defining equations of the variety and the relations among them, called syzygies, heavily depend on the algebraic and geometric structure of the variety as well as the properties of the embedding line bundle.

The lecture will be focused on the Castelnuovo-Mumford regularity bounds of algebraic varieties. We start with basic definitions, then discuss several fundamental results and methods, and conclude with possible problems and conjectures. The lecture materials are subject to change as time goes on.

Topics on Castelnuovo-Mumford regularity：

• Basic definitions, properties and examples.

• Castelnuovo-Mumford regularity bounds for points, curves, surfaces,

and higher dimensional varieties.

• The method of generic projection, vanishing theorems, generic linkages, and multiplier ideals.

Requirements: The lecture requires knowing the basic definitions contained in Chapter 2 and 3 of Hartshorne's Algebraic Geometry and Chapter 1 and 2 of Lazarsfeld's Positivity in Algebraic Geometry I (such as varieties, sheaves, cohomology groups, vector bundles, ample line bundles, and etc.)

讲座联系人/Contact:

理学院 王老师  wangqiuhui@westlake.edu.cn