Generic freeness of local cohomology and graded specialization

Chardin, Marc; Cid-Ruiz, Yairon; Simis, Aron

doi:10.1090/tran/8316

Generic freeness of local cohomology and graded specialization
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by Marc Chardin, Yairon Cid-Ruiz and Aron Simis PDF

Trans. Amer. Math. Soc. 375 (2022), 87-109 Request permission

Abstract:

The main focus is the generic freeness of local cohomology modules in a graded setting. The present approach takes place in a quite nonrestrictive setting, by solely assuming that the ground coefficient ring is Noetherian. Under additional assumptions, such as when the latter is reduced or a domain, the outcome turns out to be stronger. One important application of these considerations is to the specialization of rational maps and of symmetric and Rees powers of a module.

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