On the even-order vanishing of Jacobian theta functions

DOI10.1215/S0012-7094-84-05106-8zbMath0583.14017MaRDI QIDQ1070004

John D. Fay

Publication date: 1984

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Jacobi varietiesdouble coveringsthetanullwertevanishing property

Mathematics Subject Classification ID

Theta functions and abelian varieties (14K25) Coverings in algebraic geometry (14E20) Elliptic functions and integrals (33E05) Riemann surfaces (30F99)

Related Items (17)

New elliptic potentials ⋮ Torsion points on Jacobians of quotients of Fermat curves and \(p\)-adic soliton theory ⋮ Characterization of Jacobian varieties in terms of soliton equations ⋮ Short eigenvectors and multidimensional theta functions ⋮ Generic Torelli and local Schottky theorems for Jacobian elliptic surfaces ⋮ The algebraic-geometric AKNS potentials ⋮ Abelian pole systems and Riemann-Schottky-type problems ⋮ Singular spin structures and superstrings ⋮ The surface \(C\)-\(C\) on Jacobi varieties and 2nd order theta functions ⋮ Jacobi inversion on strata of the Jacobian of the \(C_{rs}\) curve \(y^r = f(x)\). II ⋮ Higher-order analogues of the unitarity condition for quantum \(R\)-matrices ⋮ Integrable discrete Schrödinger equations and a characterization of Prym varieties by a pair of quadrisecants ⋮ Exceptional coverings and sums of 4 triangular numbers ⋮ Riemann surfaces and their associated Wirtinger varieties ⋮ Jacobi inversion on strata of the Jacobian of the \(C_{rs}\) curve \(y^r = f(x)\) ⋮ Second order theta divisors on Pryms ⋮ Rank one elliptic \(A\)-modules and \(A\)-harmonic series

Cites Work

• Precise variational formulas for Abelian differentials
• A new compactification of the Siegel space and degeneration of abelian varieties. I
• A new compactification of the Siegel space and degeneration of Abelian varieties. II
• Prym varieties and Schottky problem
• Theta functions on Riemann surfaces
• Period relations of Schottky type on Riemann surfaces
• On Generalized Theta Functions
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