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 |