Powers of sums and their associated primes

Abstract

Let $A,B$ be polynomial rings over a field $k$, and $I\subseteq A,J\subseteq B$ proper homogeneous ideals. We analyze the associated primes of powers of $I+J\subseteq A{\otimes }_{k}B$ given the data on the summands. The associated primes of large enough powers of $I+J$ are determined. We then answer positively a question about the persistence property of $I+J$ in many new cases.

20 pages. Revised version that some minor errors are corrected

References in corpus (2)

• Symbolic powers of sums of ideals
• Tensor-Multinomial Sums of Ideals: Primary Decompositions and Persistence of Associated Primes