Characterizations of Jacobians of curves with automorphisms

DOI10.1090/S0002-9947-2010-05029-9zbMath1209.14027OpenAlexW2002858153MaRDI QIDQ3053477

Rubí E. Rodríguez, Esteban Gómez González, José María Muñoz Porras, Francisco Jose Plaza Martín

Publication date: 29 October 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2010-05029-9

zbMATH Keywords

abelian varietiestheta functionsalgebraic curvesJacobiansKP hierarchySchottky problemcompletely integrable Hamiltonian systemsKrichever correspondenceinfinite GrassmanniansBaker-Akhieser functions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Jacobians, Prym varieties (14H40) Theta functions and abelian varieties (14K25) Automorphisms of curves (14H37) Theta functions and curves; Schottky problem (14H42)

Cites Work

• Integrable discrete Schrödinger equations and a characterization of Prym varieties by a pair of quadrisecants
• Characterizing Jacobians via trisecants of the Kummer variety
• Loop groups and equations of KdV type
• Characterization of Jacobian varieties in terms of soliton equations
• Prym varieties and integrable systems
• Prym varieties, curves with automorphisms and the Sato Grassmannian
• Equations of the moduli of pointed curves in the infinite Grassmannian.
• Pfaff \(\tau\)-functions
• Theta functions on Riemann surfaces
• Cohomological structure in soliton equations and Jacobian varieties
• The Krichever map, vector bundles over algebraic curves, and Heisenberg algebras
• Equations of Hurwitz schemes in the infinite Grassmannian
• METHODS OF ALGEBRAIC GEOMETRY IN THE THEORY OF NON-LINEAR EQUATIONS
• The n-component KP hierarchy and representation theory
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