Gröbner deformations and F‐singularities

Mitra Koley and Matteo Varbaro

Mathematische Nachrichten, 2023, vol. 296, issue 7, 2903-2917

Abstract: For polynomial ideals in positive characteristic, defining F‐split rings and admitting a squarefree monomial initial ideal are different notions. In this note, we show that, however, there are strong interactions in both directions. Moreover, we provide an overview on which F‐singularities are Gröbner deforming. Also, we prove the following characteristic‐free statement: If p$\mathfrak {p}$ is a height h prime ideal such that in(p(h))$\mathrm{in}(\mathfrak {p}^{(h)})$ contains at least one squarefree monomial, then in(p)$\mathrm{in}(\mathfrak {p})$ is a squarefree monomial ideal.

Date: 2023
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https://doi.org/10.1002/mana.202100459

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