An algorithm for computing compatibly Frobenius split subvarieties

Abstract

Let $R$ be a ring of prime characteristic $p$, and let $F_{\ast }^{e}R$ denote $R$ viewed as an $R$-module via the $e$th iterated Frobenius map. Given a surjective map $\varphi :F_{\ast }^{e}R\to R$ (for example a Frobenius splitting), we exhibit an algorithm which produces all the $\varphi$-compatible ideals. We also explore a variant of this algorithm under the hypothesis that $\varphi$ is not necessarily a Frobenius splitting (or even surjective). This algorithm, and the original, have been implemented in Macaulay2.

15 pages, many statements clarified and numerous other substantial improvements to the exposition (thanks to the referees). To appear in the Journal of Symbolic Computation

References in corpus (1)

• Frobenius splitting, point-counting, and degeneration

Cited by in corpus (1)

• Compatibly split subvarieties of the Hilbert scheme of points in the plane