Associated primes of local cohomology after adjoining indeterminates

作者：Robbins Hannah^*

来源：Journal of Pure and Applied Algebra, 2014, 218(11): 2072-2080.

DOI：10.1016/j.jpaa.2014.03.005

Let A be a domain finitely generated as an algebra over a field, k, of characteristic zero, R = A[t(1), ... , t(n)] or A[[t(1), ... , t(n)]] and I subset of R any ideal. If A has a resolution of singularities, Y-0, which is the blowup of A along an ideal of depth at least two and is covered by either two or three open affines with H-j (Y-0, O-Y0) of finite length over A for j > 0, we prove that Ass(R) H-I(i)(R) is finite for every i. In particular this holds when A is a two or three dimensional normal domain with an isolated singularity which is finitely generated over a field of characteristic 0.

• 出版日期2014-11