PreprintarXiv licencearXiv
Deciding superellipticity and computing the Weierstrass normal form
Abstract
Let ๐ฎg,n โ โณg be the locus of curves of genus g โฅ 2 admitting a model yn = h(x) with h separable; such curves C have a cyclic group Cn โค Aut(C) of order n with C/Cn โ โ1. % We give an algorithm which, given an absolutely irreducible plane model F(x,y) = 0 of a curve C over a field k0 of characteristic zero, decides for which n the curve lies in ๐ฎg,n and returns a model yn = h(x) together with the birational transformation to it.
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BibTeX
@misc{shaska2026deciding,
title = {{Deciding superellipticity and computing the Weierstrass normal form}},
author = {T. Shaska},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00672},
eprint = {2609.00672},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00672},
}
RIS
TY - UNPB
TI - Deciding superellipticity and computing the Weierstrass normal form
AU - T. Shaska
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00672
UR - https://arxiv.org/abs/2609.00672
AB - Let ๐ฎ_g,n โ โณ_g be the locus of curves of genus g โฅ 2 admitting a model y^n = h(x) with h separable; such curves C have a cyclic group C_n โค Aut(C) of order n with C/C_n โ
โ^1. % We give an algorithm which, given an absolutely irreducible plane model F(x,y) = 0 of a curve C over a field k_0 of characteristic zero, decides for which n the curve lies in ๐ฎ_g,n and returns a model y^n = h(x) together with the birational transformation to it.
ER -