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arXiv · 1501.06038

Depth and regularity of powers of sums of ideals

Huy Tai Ha·Ngo Viet Trung·Tran Nam Trung
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Abstract

Given arbitrary homogeneous ideals $I$ and $J$ in polynomial rings $A$ and $B$ over a field $k$, we investigate the depth and the Castelnuovo-Mumford regularity of powers of the sum $I+J$ in $A \otimes_k B$ in terms of those of $I$ and $J$. Our results can be used to study the behavior of the depth and regularity functions of powers of an ideal. For instance, we show that such a depth function can take as its values any infinite non-increasing sequence of non-negative integers.

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Huy Tai Ha, Ngo Viet Trung, Tran Nam Trung. 2016-01-01. Depth and regularity of powers of sums of ideals. https://doi.org/10.1007/s00209-015-1566-9

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