Symbolic powers and free resolutions of generalized-申伊塃副教授（中国科学技术大学）

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.