STABLE BEHAVIOR OF FROBENIUS POWERS OVER A GENERAL HYPERSURFACE

Claudia Miller, Hamidreza Rahmati, R. G. Rebecca

Research output: Contribution to journalArticlepeer-review

Abstract

The main goal of this paper is to prove, in positive characteristic p, stability behavior for the graded Betti numbers in the periodic tails of the minimal resolutions of Frobenius powers of the homogeneous maximal ideals for very general choices of hypersurface in three variables whose degree has the opposite parity to that of p. We also find some of the structure of the matrix factorization giving the resolution. We achieve this by developing a method for obtaining the degrees of the generators of the defining ideal of an c-compressed Gorenstein Artinian graded algebra from its socle degree, where c is a Frobenius power of the homogeneous maximal ideal. As an application, we also obtain the Hilbert–Kunz function of the hypersurface ring, as well as the Castelnuovo–Mumford regularity of the quotients by Frobenius powers of the homogeneous maximal ideal.

Original languageEnglish (US)
Pages (from-to)1350-1393
Number of pages44
JournalTransactions of the American Mathematical Society Series B
Volume11
DOIs
StatePublished - 2024

Keywords

  • Artinian algebras
  • Free resolutions
  • Frobenius powers
  • Inverse systems
  • Positive characteristic
  • Relatively compressed algebras

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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