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线上学术报告

Title: Symbolic powers and free resolutions of generalized

star configurations of hypersurfaces

Speaker: 申伊塃 副教授（中国科学技术大学）

Abstract

This is joint work with Kuei-Nuan Lin. As a generalization of the ideals of star configurations of hypersurfaces, we consider the $a$-fold product ideal $I_a(f_1^{m_1}\cdots f_s^{m_s})$ when $f_1,\dots,f_s$ is a sequence of $n$-generic forms in a polynomial ring and $1\le a\le m_1+\cdots+m_s$.  Firstly, we show that this ideal has complete intersection quotients when these forms are of the same degree and essentially linear. Then, we study its symbolic powers while focusing on the uniform case with $m_1=\cdots=m_s$.  For large $a$, we compute the projective dimension and Castelnuovo-Mumford regularity of symbolic powers of $I$. We also compute its resurgence and symbolic defect. Related Harbourne-Huneke containment problem and  Demailly-like bound are considered as well. Finally, we show that these symbolic powers are sequentially Cohen-Macaulay.

报告人简介：申伊塃，1996-2002年在武汉大学数学系学习，获学士、硕士学位，2002 - 2009年在普渡大学数学系学习，获博士学位。从2009年起，就职于中国科学技术大学数学系，历任讲师、副教授。主要研究交换代数和代数组合等领域，有系列研究成果发表在J. Algebra，J. Algebraic Combin.，Nagoya Math. J.等国际知名杂志上。

北京时间：2022年10月13日（周四）上午10:10-11:10

腾讯会议：770-3833-5039  会议密码:  202210

入会链接:  https://meeting.tencent.com/dm/KDcuUQFL08o8

联系人:  惠昌常 陈红星