Equations of the moduli of pointed curves in the infinite Grassmannian

@article{Porras1997EquationsOT,
  title={Equations of the moduli of pointed curves in the infinite Grassmannian},
  author={J. M. Mu{\~n}oz Porras and Francisco Jos'e Plaza Mart'in},
  journal={Journal of Differential Geometry},
  year={1997},
  volume={51},
  pages={431-469}
}
The main result of this paper is the explicit computa- tion of the equations defining the moduli space of triples (C,p,�), where C is an integral and complete algebraic curve, p a smooth rational point anda certain isomorphism. This is achieved by introducing algebraically infinite Grassmannians, tau and Baker- Ahkiezer functions and by proving an Addition Formula for tau functions. 
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References

SHOWING 1-10 OF 41 REFERENCES
PRYM VARIETIES AND THE INFINITE GRASSMANNIAN
In this paper we study Prym varieties and their moduli space using the well-known techniques of the infinite Grassmannian. There are three main results of this paper: a new definition of the BKP…
Intersection theory on the moduli space of curves and the matrix airy function
We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical…
METHODS OF ALGEBRAIC GEOMETRY IN THE THEORY OF NON-LINEAR EQUATIONS
CONTENTSIntroduction § 1. The Akhiezer function and the Zakharov-Shabat equations § 2. Commutative rings of differential operators § 3. The two-dimensional Schrodinger operator and the algebras…
Formal groups and conformal field theory over Z
Quantum field theory, Grassmannians, and algebraic curves
This paper is devoted in part to clarifying some aspects of the relation between quantum field theory and infinite Grassmannians, and in part to pointing out the existence of a close analogy between…
The algebraic formalism of soliton equations over arbitrary base fields
The aim of this paper is to offer an algebraic construction of infinite-dimensional Grassmannians and determinant bundles (and therefore valid for arbitrary base fields). As an application we…
Grassmannian of $k((z))$: Picard Group, Equations and Automorphisms
Abstract. This paper aims at generalizing some geometric prop-erties of Grassmannians of finite dimensional vector spaces to thecase of Grassmannnians of infinite dimensional ones, in particularfor…
Geometric realization of conformal field theory on Riemann surfaces
Conformal field theory on a family of Riemann surfaces is formulated. We derive equations of motion of vacua which are parametrized by moduli of Riemann surfaces and show that these vacua are…
Theta Functions on Riemann Surfaces
Riemann's theta function.- The prime-form.- Degenerate Riemann surfaces.- Cyclic unramified coverings.- Ramified double coverings.- Bordered Riemann surfaces.
Cohomological structure in soliton equations and Jacobian varieties
On etudie la structure des orbites du systeme dynamique definie par la hierarchie KP totale. On montre que chaque orbite est localement isomorphe a un certain groupe de cohomologie associe a une…
...
...