Some explicit arithmetics on curves of genus three and their applications
A Richelot isogeny between Jacobian varieties is an isogeny whose kernel is included in the
$2 $-torsion subgroup of the domain. In particular, a Richelot isogeny whose codomain is …
$2 $-torsion subgroup of the domain. In particular, a Richelot isogeny whose codomain is …
Reduction of Plane Quartics and Cayley Octads
R van Bommel, J Docking, V Dokchitser… - arXiv preprint arXiv …, 2023 - arxiv.org
We give a conjectural characterisation of the stable reduction of plane quartics over local
fields in terms of their Cayley octads. This results in p-adic criteria that efficiently give the …
fields in terms of their Cayley octads. This results in p-adic criteria that efficiently give the …
Models of hyperelliptic curves with tame potentially semistable reduction
O Faraggi, S Nowell - Transactions of the London Mathematical …, 2020 - Wiley Online Library
Let C be a hyperelliptic curve y 2= f (x) over a discretely valued field K. The p‐adic distances
between the roots of f (x) can be described by a completely combinatorial object known as …
between the roots of f (x) can be described by a completely combinatorial object known as …
Reduction of Plane Quartics and Dixmier-Ohno invariants
R van Bommel, J Docking, R Lercier… - arXiv preprint arXiv …, 2024 - arxiv.org
Reduction of Plane Quartics and Dixmier-Ohno invariants Page 1 REDUCTION OF PLANE
QUARTICS AND DIXMIER-OHNO INVARIANTS RAYMOND VAN BOMMEL, JORDAN …
QUARTICS AND DIXMIER-OHNO INVARIANTS RAYMOND VAN BOMMEL, JORDAN …
Integral differential forms for superelliptic curves
S Kunzweiler, S Wewers - arXiv preprint arXiv:2003.12357, 2020 - arxiv.org
Given a superelliptic curve $ Y_K: y^ n= f (x) $ over a local field $ K $, we describe the
theoretical background and an implementation of a new algorithm for computing the …
theoretical background and an implementation of a new algorithm for computing the …
Invariants for trees of non-archimedean polynomials and skeleta of superelliptic curves
PA Helminck - Mathematische Zeitschrift, 2022 - Springer
In this paper we generalize the j-invariant criterion for the semistable reduction type of an
elliptic curve to superelliptic curves X given by y^ n= f (x) yn= f (x). We first define a set of …
elliptic curve to superelliptic curves X given by y^ n= f (x) yn= f (x). We first define a set of …
Arithmetic of genus three curves and their Jacobians
J Docking - 2023 - discovery.ucl.ac.uk
The Birch–Swinnerton-Dyer Conjecture predicts that, given an abelian variety A over a
number field K, its rank, rk (A/K), is equal to the order of vanishing of its L-function L (A/K, s) …
number field K, its rank, rk (A/K), is equal to the order of vanishing of its L-function L (A/K, s) …
A generalization of the Newton-Puiseux algorithm for semistable models
PA Helminck - arXiv preprint arXiv:2007.09449, 2020 - arxiv.org
In this paper we give an algorithm that calculates the skeleton of a tame covering of curves
over a complete discretely valued field. The algorithm relies on the {{tame simultaneous …
over a complete discretely valued field. The algorithm relies on the {{tame simultaneous …
On invariants of Artin-Schreier curves
J Duque-Rosero, H Goodson, EL García… - arXiv preprint arXiv …, 2024 - arxiv.org
The main goal of this article is to expand the theory of invariants of Artin-Schreier curves by
giving a complete classification in genus 3 and 4. To achieve this goal, we first establish …
giving a complete classification in genus 3 and 4. To achieve this goal, we first establish …
On the maximality of hyperelliptic Howe curves of genus 3
R Ohashi - Kodai Mathematical Journal, 2022 - jstage.jst.go.jp
ON THE MAXIMALITY OF HYPERELLIPTIC HOWE CURVES OF GENUS 3 Ryo Ohashi
Abstract 1. Introduction Throughout this paper, a curve alw Page 1 R. OHASHI KODAI MATH. J …
Abstract 1. Introduction Throughout this paper, a curve alw Page 1 R. OHASHI KODAI MATH. J …