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arXiv · 1210.6616

Bounds for the regularity of local cohomology of bigraded modules

Jürgen Herzog·Ahad Rahimi
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Abstract

Let $M$ be a finitely generated bigraded module over the standard bigraded polynomial ring $S=K[x_1,...,x_m, y_1,...,y_n]$, and let $Q=(y_1,...,y_n)$. The local cohomology modules $H^k_Q(M)$ are naturally bigraded, and the components $H^k_Q(M)_j=\Dirsum_iH^k_Q(M)_{(i,j)}$ are finitely generated graded $K[x_1,...,x_m]$-modules. In this paper we study the regularity of $H^k_Q(M)_j$, and show in several cases that $\reg H^k_Q(M)_j$ is linearly bounded as a function of $j$.

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Jürgen Herzog, Ahad Rahimi. 2012-10-24. Bounds for the regularity of local cohomology of bigraded modules. https://arxiv.org/abs/1210.6616

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