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Equations of the moduli of pointed curves in the infinite Grassmannian. (English) Zbl 1065.14512

Summary: The main result of this paper is the explicit computation of the equations defining the moduli space of triples \((C,p,\phi)\), where \(C\) is an integral and complete algebraic curve, \(p\) a smooth rational point and \(\phi\) a certain isomorphism. This is achieved by introducing algebraically infinite Grassmannians, tau and Baker-Akhiezer functions and by proving an addition formula for tau functions.

MSC:

14H70 Relationships between algebraic curves and integrable systems
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14H42 Theta functions and curves; Schottky problem
14L15 Group schemes
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
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