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Mathematics > Algebraic Geometry

arXiv:2206.00420 (math)
[Submitted on 1 Jun 2022 (v1), last revised 3 Oct 2024 (this version, v3)]

Title:Tropical invariants for binary quintics and reduction types of Picard curves

Authors:Paul Alexander Helminck, Yassine El Maazouz, Enis Kaya
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Abstract:We express the reduction types of Picard curves in terms of tropical invariants associated to binary quintics. We also give a general framework for tropical invariants associated to 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 $\overline{M}_{0,n}$.
Comments: 25 pages
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
MSC classes: 14T20, 13A50, 11G20
Cite as: arXiv:2206.00420 [math.AG]
  (or arXiv:2206.00420v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2206.00420
Journal reference: Glasgow Mathematical Journal , Volume 66 , Issue 1 , January 2024 , pp. 65 - 87
Related DOI: https://doi.org/10.1017/S0017089523000344

Submission history

From: Yassine El Maazouz [view email]
[v1] Wed, 1 Jun 2022 11:54:17 UTC (276 KB)
[v2] Fri, 22 Sep 2023 16:53:14 UTC (34 KB)
[v3] Thu, 3 Oct 2024 19:45:08 UTC (34 KB)
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