Powers of ideals: the case of mixed sums

Thời gian: 09:30 đến 10:30 Ngày 28/04/2016

Địa điểm: C2-714

Tóm tắt:

The study of asymptotic properties of powers of ideals is a classical topic in commutative algebra. We will discuss this problem with focus on the following case: Let J and L be homogeneous ideals living in different polynomial rings R_1 and R_2 over a field k. Let R be the tensor product over k of R_1 and R_2 and I be the sum of J and L in R. With mild assumptions on the field, we provide explicit computation of the depth and regularity of any power of I in terms of that of the powers of J and L. In particular, these computations enable us to improve recent results due to Hà, N.V. Trung and T.N. Trung.