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arXiv · 2005.14643

Computing generalized Frobenius powers of monomial ideals

Christopher A. Francisco·Matthew Mastroeni·Jeffrey Mermin·Jay Schweig
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Abstract

Generalized Frobenius powers of an ideal were introduced in work of Hern\'andez, Teixeira, and Witt as characteristic-dependent analogs of test ideals. However, little is known about the Frobenius powers and critical exponents of specific ideals, even in the monomial case. We describe an algorithm to compute the critical exponents of monomial ideals and use this algorithm to prove some results about their Frobenius powers and critical exponents. Rather than using test ideals, our algorithm uses techniques from linear optimization.

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Christopher A. Francisco, Matthew Mastroeni, Jeffrey Mermin, Jay Schweig. 2020-05-29. Computing generalized Frobenius powers of monomial ideals. https://arxiv.org/abs/2005.14643

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