Holomorphic differentials of alternating four covers

Frauke M Bleher; Margarita Bustos Gonzalez

doi:10.48550/arxiv.2510.15743

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Holomorphic differentials of alternating four covers

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Holomorphic differentials of alternating four covers

Frauke M Bleher and Margarita Bustos Gonzalez

ArXiv.org

Cornell University

10/17/2025

DOI: 10.48550/arxiv.2510.15743

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

Suppose k is an algebraically closed field of characteristic two, let A4 be an alternating group on four letters, and let H be the unique Sylow two-subgroup of A4. Let X be a smooth projective irreducible curve over k with a faithful A4-action such that the quotient curve X/H is a projective line and the H-cover X → X/H is totally ramified, in the sense that it is ramified and every branch point is totally ramified. Under these assumptions, we determine the precise kA4-module structure of the space of holomorphic differentials of X over k. We show that there are infinitely many different isomorphism classes of indecomposable kA4-modules that can occur as direct summands, and we give precise formulas for the multiplicities with which they occur.

Mathematics - Algebraic Geometry

Mathematics - Number Theory

Details

Title: Subtitle: Holomorphic differentials of alternating four covers
Creators: Frauke M Bleher
Margarita Bustos Gonzalez
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2510.15743
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 10/17/2025
Academic Unit: Mathematics
Record Identifier: 9985016017002771

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