F. J. Plaza Martín

Automorphism Group of k((t)):¶Applications to the Bosonic String

This paper is concerned with the formulation of a non-pertubative theory of the bosonic string. We introduce a formal group G which we propose as the “universal moduli space” for such a formulation. This is motivated because G establishes a natural link between representations of the Virasoro algebra and the moduli space of curves.Abstract: This paper is concerned with the formulation of a non-pertubative theory of the bosonic string. We introduce a formal group G which we propose as the “universal moduli space” for such a formulation. This is motivated because G establishes a natural link between representations of the Virasoro algebra and the moduli space of curves.

Addition formulae for non-Abelian theta functions and applications

This paper generalizes for non-Abelian theta functions a number of formulae valid for theta functions of Jacobian varieties. The addition formula, the relation with the Szego kernel and with the multicomponent KP hierarchy and the behavior under cyclic coverings are given.

Algebraic solutions of the multicomponent KP hierarchy

It is shown that it is possible to write down tau functions for the n-component KP hierarchy in terms of non-abelian theta functions. This is a generalization of the rank 1 situation; that is, the relation of theta functions of Jacobians and tau functions for the KP hierarchy.

PRYM VARIETIES, CURVES WITH AUTOMORPHISMS AND THE SATO GRASSMANNIAN

AbstractThe aim of the paper is twofold. First, some results of Shiota and Plaza-Martín on Prym varieties of curves with an involution are generalized to the general case of an arbitrary automorphism of prime order. Second, the equations defining the moduli space of curves with an automorphism of prime order as a subscheme of the Sato Grassmannian are given.

EQUATIONS OF THE MODULI OF HIGGS PAIRS AND INFINITE GRASSMANNIAN

In this paper the moduli space of Higgs pairs over a fixed smooth projective curve with extra formal data is defined and is endowed with a scheme structure. We introduce a relative version of the Krichever map using a fibration of Sato Grassmannians and show that this map is injective. This, together with the characterization of the points of the image of the Krichever map, allows us to prove that this moduli space is a closed subscheme of the product of the moduli of vector bundles (with formal extra data) and a formal anologue of the Hitchin base. This characterization also provides us with a method for explicitly computing KP-type equations that describe the moduli space of Higgs pairs. Finally, for the case where the spectral cover is totally ramified at a fixed point of the curve, these equations are given in terms of the characteristic coefficients of the Higgs field.

Quotients on the Sato Grassmannian and the moduli of vector bundles

It is shown that there exists a geometric quotient of the subscheme of stable points of Gr(C((z)) ⊕r ) under the action of Sl(r, C). The consequences in terms of vector bundles on an algebraic curve are studied.