代数几何讨论班

报告人：朱智贤 (首都师范大学 交叉科学研究院)

报告时间:  2022年12月5日，12月12日，12月19日

(周一)上午10：00-11:00

腾讯会议号：617-7175-6687 密码: 202212

报告题目: An introduction to Fujita conjecture

报告摘要:

Linear series have long played a central role in algebraic geometry. On smooth projective varieties, one would like to know the positivity of the adjoint line bundles and pluri-canonical line bundles. In this series of lectures, we focus on Fujita’s freeness conjecture and very ampleness conjecture on the adjoint line bundles.

Lecture 1 （2022年12月05日）. We first introduce Fujita’s conjectures and give a brief overview of the history and current status. Then we present Reider’s method, which involves Bogomolov’s inequality, to show both conjectures hold on algebraic surfaces.  

Lecture 2（2022年12月12日）. Fujita’s very ampleness conjecture is still open in dimension 3. The freeness conjecture has been proved up to dimension 5 by vanishing theorems. We start with reviewing some basic facts on singularity theory in birational geometry. Then we show how to apply it to prove the Fujita freeness conjecture in dimension 4.

Lecture 3（2022年12月19日）. Reider’s result on the surface proved a stronger version of Fujita’s conjectures. In dimension 3, Helmke developed a volume trick and proved the freeness conjecture under a numerical weaker condition. We briefly explain Helmke’s method and combine it with the singularity method to explain our dim 5 result. If time permits, we discuss asymptotic results on Fujita’s conjectures.

报告人简介:

朱智贤, 美国密歇根大学数学专业博士毕业，现任首都师范大学副研究员。研究方向是代数几何。已在Adv.Mat, Math.Z., J.Pure Appl.Algebra等著名期刊发表论文。

邀请人：陈伊凡