THE SIGMA FUNCTION FOR WEIERSTRASS SEMIGROUPS 〈3, 7, 8〉 AND 〈6, 13, 14, 15, 16〉

DOI10.1142/S0129167X13500857zbMath1284.14045arXiv1303.0451OpenAlexW2037763845MaRDI QIDQ5396078

Emma Previato, Jiryo Komeda, Shigeki Matsutani

Publication date: 5 February 2014

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.0451

zbMATH Keywords

Weierstrass semigroupKleinian \(\sigma\)-functionNorton numbers

Mathematics Subject Classification ID

Plane and space curves (14H50) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Riemann surfaces; Weierstrass points; gap sequences (14H55)

Related Items (10)

On Jacobi inversion formulae for telescopic curves ⋮ Periods of second kind differentials of $(n,s)$-curves ⋮ The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications ⋮ Unnamed Item ⋮ The sigma function for trigonal cyclic curves ⋮ The \(\operatorname{al}\) function of a cyclic trigonal curve of genus three ⋮ Space curves and solitons of the KP hierarchy. I: The \(l\)-th generalized KdV hierarchy ⋮ The Riemann constant for a non-symmetric Weierstrass semigroup ⋮ Commuting ordinary differential operators and the Dixmier test ⋮ Complementary modules of Weierstrass canonical forms

Cites Work

• Unnamed Item
• Unnamed Item
• Séminaire sur les singularités des surfaces. Centre de Mathématiques de l'École Polytechnique, Palaiseau 1976-1977
• On algebraic expressions of sigma functions for (\(n, s\)) curves
• A class of solutions of the dispersionless KP equation
• Configurations of lines and models of Lie algebras
• Jacobi inversion on strata of the Jacobian of the \(C_{rs}\) curve \(y^r = f(x)\)
• Existence, decomposition, and limits of certain Weierstrass points
• The Milnor number and deformations of complex curve singularities
• On primitive Schubert indices of genus \(g\) and weight \(g-1\)
• Construction of elliptic curves with high rank via the invariants of the Weyl groups
• Weierstrass points and monomial curves
• Fuchsian groups, automorphic functions and Schwarzians
• Theta functions on Riemann surfaces
• Harmonic spinors
• On higher genus Weierstrass sigma-function
• Rational analogues of Abelian functions.
• Cohomological structure in soliton equations and Jacobian varieties
• Riemann surfaces and the theta function
• Existence of the non-primitive Weierstrass gap sequences on curves of genus 8
• Del Pezzo surfaces of degree 1 and Jacobians
• Generators and relations of abelian semigroups and semigroup rings
• Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen
• Hyperelliptic solutions of KdV and KP equations: re-evaluation of Baker's study on hyperelliptic sigma functions
• Sigma, tau and Abelian functions of algebraic curves
• Numerical Semigroups that Differ from a Symmetric Numerical Semigroup in One Element
• DETERMINANT EXPRESSIONS FOR HYPERELLIPTIC FUNCTIONS
• Monstrous Moonshine
• More on replicable functions
• Solution of the dispersionless Hirota equations
• σ-functions of (n,s)-curves
• Existence of the primitive Weierstrass gap sequences on curves of genus 9
• A Generalization of a Formula of Eisenstein
• Notes on Coxeter Transformations and the McKay Correspondence
• On Faber Polynomials
• Uniformization of Jacobi varieties of trigonal curves and nonlinear differential equations
• Twelve points on the projective line, branched covers, and rational elliptic fibrations

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