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We introduce an invariant, associated to a coherent sheaf of graded modules over a projective morphism of schemes, which controls when sheaf cohomology can be passed through the given morphism.… Click to show full abstract
We introduce an invariant, associated to a coherent sheaf of graded modules over a projective morphism of schemes, which controls when sheaf cohomology can be passed through the given morphism. We then use this invariant to estimate the stability indexes of the regularity and a ∗ -invariant of powers of homogeneous ideals. Specifically, for an equigenerated homogeneous ideal I in a standard graded algebra over a Noetherian ring, we give bounds for the smallest values of power q starting from which a ∗ ( I q ) and reg( I q ) become linear functions.
Journal Title: Acta Mathematica Vietnamica
Year Published: 2019
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