On maximal curves

DOI10.1006/jnth.1997.2148zbMath0914.11036arXivalg-geom/9610023OpenAlexW1972945993MaRDI QIDQ1376254

Arnaldo Garcia, Rainer Fuhrmann, Fernando Torres

Publication date: 18 December 1997

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9610023

zbMATH Keywords

Hermitian curvemaximal curveWeierstrass point

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Global ground fields in algebraic geometry (14G25)

Related Items (40)

Quotient curves of the GK curve ⋮ The $a$-number of jacobians of certain maximal curves ⋮ Some Maximal Function Fields and Additive Polynomials ⋮ On maximal curves related to Chebyshev polynomials ⋮ On some open problems on maximal curves ⋮ Weierstrass semigroups for maximal curves realizable as Harbater-Katz-Gabber covers ⋮ Superspecial curves of genus 4 in small characteristic ⋮ On the order sequence of an embedding of the Ree curve ⋮ Rational points on cubic, quartic and sextic curves over finite fields ⋮ On maximal curves which are not Galois subcovers of the Hermitian curve ⋮ Optimal and maximal singular curves ⋮ Weierstrass semigroups and automorphism group of a maximal curve with the third largest genus ⋮ On the curve \(Y^n= X^{\ell}(X^m + 1)\) over finite fields ⋮ Maximal curves and Tate-Shafarevich results for quartic and sextic twists ⋮ Fast enumeration of superspecial hyperelliptic curves of genus 4 with automorphism group \(V_4\) ⋮ On Kummer covers with many rational points over finite fields. ⋮ On subfields of the Hermitian function field involving the involution automorphism ⋮ A note on certain maximal curves ⋮ On space maximal curves ⋮ Irreducible canonical representations in positive characteristic ⋮ A new family of maximal curves over a finite field ⋮ A generalization of the Giulietti–Korchmáros maximal curve ⋮ A quotient curve of the Fermat curve of degree twenty-three attaining the Serre bound ⋮ Zeta function of the projective curve \(aY^{2l}= bX^{2l}+ cZ^{2l}\) over a class of finite fileds, for odd primes ⋮ On maximal curves and linearized permutation polynomials over finite fields ⋮ On the spectrum for the genera of maximal curves over small fields ⋮ Curves covered by the Hermitian curve ⋮ Further examples of maximal curves ⋮ On the curve \(y^n = x^m + x\) over finite fields ⋮ \(\mathbb{F}_{p^2}\)-maximal curves with many automorphisms are Galois-covered by the Hermitian curve ⋮ The curve \(y^n=x^\ell(x^m+1)\) over finite fields. II ⋮ Quadratic forms of codimension 2 over finite fields containing \(\mathbb F_4\) and Artin-Schreier type curves ⋮ On a characterization of certain maximal curves ⋮ On the existence of superspecial and maximal nonhyperelliptic curves of genera four and five ⋮ On maximal curves with Frobenius dimension 3 ⋮ Classification of all Galois subcovers of the Skabelund maximal curves ⋮ On curves covered by the Hermitian curve. ⋮ Weierstrass semigroup at \(m+1\) rational points in maximal curves which cannot be covered by the Hermitian curve ⋮ Computational approach to enumerate non-hyperelliptic superspecial curves of genus 4 ⋮ Curves of large genus covered by the hermitian curve

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algebraic function fields and codes
• Places of degree one in function fields over finite fields
• Weierstrass points on certain non-classical curves
• The uniform position principle for curves in characteristic p
• Frobenius non classical curves
• On rational points of curves of genus 3 over finite fields
• The genus of maximal function fields over finite fields
• Elementary abelian \(p\)-extensions of algebraic function fields
• The genus of curves over finite fields with many rational points
• Group codes on certain algebraic curves with many rational points
• Endomorphisms of Abelian varieties over finite fields
• Zur arithmetischen Theorie der algebraischen Funktionen. II: Allgemeine Theorie der Weierstraßpunkte
• ALGEBRAICO-GEOMETRIC CODES
• Weierstrass Points and Curves Over Finite Fields
• A characterization of Hermitian function fields over finite fields.
• How to Construct Curves over Finite Fields With Many Points
• Linear systems on curves with no Weierstrass points

This page was built for publication: On maximal curves