Superspecial curves of genus 4 in small characteristic

DOI10.1016/j.ffa.2016.12.001zbMath1404.11089arXiv1607.01114OpenAlexW2963490203MaRDI QIDQ2396755

Momonari Kudo, Shushi Harashita

Publication date: 24 May 2017

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.01114

zbMATH Keywords

complete intersectionsmaximal curvessuperspecial curvesHasse-Witt matrices

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Rational points (14G05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Jacobians, Prym varieties (14H40) Curves over finite and local fields (11G20) Computational aspects of algebraic curves (14Q05)

Related Items (10)

Computing representation matrices for the action of Frobenius on cohomology groups ⋮ Automorphism groups of superspecial curves of genus 4 over \(\mathbb{F}_{11}\) ⋮ Efficient search for superspecial hyperelliptic curves of genus four with automorphism group containing \(\mathbf{C}_6\) ⋮ Fast enumeration of superspecial hyperelliptic curves of genus 4 with automorphism group \(V_4\) ⋮ Representation of non-special curves of genus 5 as plane sextic curves and its application to finding curves with many rational points ⋮ On the spectrum for the genera of maximal curves over small fields ⋮ Hasse–Witt and Cartier–Manin matrices: A warning and a request ⋮ On the existence of superspecial and maximal nonhyperelliptic curves of genera four and five ⋮ Computational approach to enumerate non-hyperelliptic superspecial curves of genus 4 ⋮ Superspecial Trigonal Curves of Genus 5

Uses Software

• Magma
• Maple
• SINGULAR

Cites Work

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• On the Jacobian varieties of hyperelliptic curves over fields of characteristic \(p>2\)
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• The Magma algebra system. I: The user language
• On maximal curves
• Hybrid approach for solving multivariate systems over finite fields
• On supersingular curves and Abelian varieties.
• The Geometry of Syzygies
• Tables of curves with many points
• New methods for bounding the number of points on curves over finite fields
• New bounds on the maximum number of points on genus-4 curves over small finite fields

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