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Tropical invariants for binary quintics and reduction types of Picard curves

Part of: General commutative ring theory Arithmetic algebraic geometry

Published online by Cambridge University Press:  06 November 2023

Paul Alexander Helminck ,
Yassine El Maazouz Open the ORCID record for Yassine El Maazouz [Opens in a new window]  and
Enis Kaya
Paul Alexander Helminck*
Affiliation:
Department of Mathematical Sciences, Durham University, Durham, UK
Yassine El Maazouz
Affiliation:
Department of Statistics, University of California Berkeley, Berkeley, CA, USA
Enis Kaya
Affiliation:
Department of Mathematics, KU Leuven, Heverlee, Belgium
*
Corresponding author: Paul Alexander Helminck; Email: yassine.el-maazouz@berkeley.edu
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Abstract

In this paper, we express the reduction types of Picard curves in terms of tropical invariants associated with binary quintics. We also give a general framework for tropical invariants associated with group actions on arbitrary varieties. The problem of finding tropical invariants for binary forms fits in this general framework by mapping the space of binary forms to symmetrized versions of the Deligne–Mumford compactification $\overline{M}_{0,n}$.

Keywords

Tropical geometryInvariant theoryPicard curvesBinary forms

MSC classification

Primary: 13A50: Actions of groups on commutative rings; invariant theory 11G20: Curves over finite and local fields

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 66 , Issue 1 , January 2024 , pp. 65 - 87
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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