An upper bound for polynomial log-volume growth of automorphisms of zero entropy

：江辰（上海数学中心）
：2023-05-22 09:00
：厦门大学海韵园实验楼110报告厅

报告人：江辰（上海数学中心）

时  间：2023年5月22日上午09:00-10:30 

地  点：厦门大学海韵园实验楼110报告厅

内容摘要:

For an automorphism f of a smooth projective variety X, Gromov introduced the log-volume growth of f and showed that it coincides with the algebraic/topological entropy of f. In order to study automorphisms of zero entropy, Cantat and Paris-Romaskevich introduced polynomial log-volume growth of f (plov for short) which turns out to be closely related to the Gelfand—Kirillov dimension of the twisted homogeneous coordinate ring associated with (X, f).

This talk will contain 2 parts: in the first part, I will give an optimal upper bound that plov(f) is at most d^2, where d is the dimension of X. This affirmatively answers questions of Cantat--Paris-Romaskevich and Lin--Oguiso--Zhang; in the second part, I will discuss the polynomial growth rate of degree sequences, and show that the growth rate is at most 2d-2, which generalizes a result of Dinh—Lin--Oguiso--Zhang. All results are based on a joint work with Fei Hu.

个人简介：

江辰，上海数学中心长聘副教授。2015年于东京大学获得博士学位，之后在东京大学、美国国家数学中心等机构从事博士后研究；2019年回国，就职于上海数学中心，并入选国家级青年人才项目。江辰的研究领域为代数几何，在Fano簇的有界性、三维簇的精细几何、自同构的多项式对数体积增长及其它关于对数Calabi-Yau簇、有理连通簇、超Kähler簇、二次曲线丛的众多问题上取得优秀的成果，已有多篇论文发表在Duke Math. J., J. Algebraic Geoemtry, J. Differential Geom., Math. Ann.等期刊。