Binomial expansion of saturated and symbolic powers of sums of ideals
Speaker: Nguyễn Đăng Hợp (Viện Toán học)

Time: 9:30 - 11:30, Feb 23, 2022

Venue: Room 302, A5, Institute of Mathematics, VAST (Online: https://meet.google.com/esi-huxm-xqg

Abstract: There are two different notions for symbolic powers of ideals existing in the literature, one defined in terms of associated primes, the other in terms of minimal primes. Elaborating on an idea known to Eisenbud, Herzog, Hibi, and Trung, we interpret both notions of symbolic powers as suitable saturations of the ordinary powers. We prove a binomial expansion formula for saturated powers of sums of ideals. This gives a uniform treatment to an array of existing and new results on both notions of symbolic powers of such sums: binomial expansion formulas, computations of depth and regularity, and criteria for the equality of ordinary and symbolic powers. Joint work with H.T. Hà, Ạ.V. Jayanthan, and A. Kumar.