On the existence of superspecial and maximal nonhyperelliptic curves of genera four and five

DOI10.1080/00927872.2019.1609013zbMath1468.14062arXiv1804.09063OpenAlexW2954557884MaRDI QIDQ5238147

Momonari Kudo

Publication date: 28 October 2019

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.09063

zbMATH Keywords

maximal curvessuperspecial curvesnonhyperelliptic curves of low genus

Mathematics Subject Classification ID

Rational points (14G05) Special algebraic curves and curves of low genus (14H45) Finite ground fields in algebraic geometry (14G15) Computational aspects of algebraic curves (14Q05)

Related Items (1)

The existence of supersingular curves of genus 4 in arbitrary characteristic

Uses Software

• Magma
• manYPoints

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on superspecial and maximal curves
• On superspecial abelian surfaces over finite fields
• A note on certain maximal hyperelliptic curves
• On the curve \(y^n = x^m + x\) over finite fields
• Class numbers of positive definite ternary quaternion Hermitian forms
• On rational points of curves of genus 3 over finite fields
• The Magma algebra system. I: The user language
• On maximal curves
• On maximal curves related to Chebyshev polynomials
• Superspecial hyperelliptic curves of genus 4 over small finite fields
• Some sextics of genera five and seven attaining the Serre bound
• Superspecial curves of genus 4 in small characteristic
• On maximal curves of Fermat type
• A note on certain maximal curves
• Newton Polygons of Cyclic Covers of the Projective Line Branched at Three Points
• On supersingular curves and Abelian varieties.
• Hunting for Curves with Many Points
• Superspecial Trigonal Curves of Genus 5

This page was built for publication: On the existence of superspecial and maximal nonhyperelliptic curves of genera four and five