报告人: Ngo Viet Trung教授
（Vietnam Academy of Science and Technology）
第三世界科学院院士、曾担任越南科学院数学研究所所长
题目: Symbolic powers of sum of ideals （I）
时间: 2017年5月9日(周二)下午3:30-4:20
地点: 维格堂119
题目: Symbolic powers of sum of ideals （II）
时间: 2017年5月9日(周二)下午4:30-5:20
地点: 维格堂119
摘要: Let I and J be nonzero ideals in two Noetherian algebras A and B over a field k. We study algebraic properties and invariants of symbolic powers of the ideal I+J in A⊗kB. Our main technical result is the binomial expansion (I +J)^(n) = /sum_{i+j=n} I^(i)J^(j) for all n > 0. Moreover, we show that if char(k) = 0 or if I is a monomial ideal, the induced maps Tor_A^i (I(n), k) → Tor_A^i (I(n−1), k) are zero for all i ≥ 0. These results allow us to establish formulas for the depth and the regularity of (I + J)^(n) and (I + J)^(n)/(I + J)^(n+1) in terms of those of I and J. Our approach has several interesting consequences on the equality between ordinary and symbolic powers, the Waldschmidt constant and the Cohen-Macaulayness of symbolic powers. In particular, we show that any convergent non-negative numerical function is the depth function of powers of a monomial ideal, which settles a conjecture of Herzog and Hibi.