Powers of ideals and the cohomology of stalks and fibers of morphisms
By Marc Chardin. 2010
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We first provide here a very short proof of a refinement of a theorem of Kodiyalam and Cutkosky, Herzog and Trung on the regularity of powers of ideals. This result implies a conjecture of H\`a and generalizes a result of Eisenbud and Harris concerning the case of ideals primary for the graded maximal ideal in a standard graded algebra over a field. It also implies a new result on the regularities of powers of ideal sheaves. We then compare the cohomology of the stalks and the cohomology of the fibers of a projective morphism to the effect of comparing the maximum over fibers and over stalks of the Castelnuovo-Mumford regularities of a family of projective schemes.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/7a5219e0bff315d0073b5fc30a1bdfd8ffc63011
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Regularity of powers of forests and cycles (2014, background): “[4, 8, 14, 15, 19]), even in simple situations such as when I is generated by general linear forms (cf.”
- Depth and regularity of powers of sums of ideals (2015, background): “For instance, see [14, 15, 17, 20, 22, 23, 26] for studies on depth of powers of ideals, and see [1, 3, 6, 7, 8, 11, 10, 13, 19, 21, 24] for studies on regularity of powers of ideals.”