%0 Report
%D 1991
%T Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory
%A Boris Dubrovin
%X We construct flat Riemannian metrics on moduli spaces of algebraic curves with marked meromorphic function. This gives a new class of exact algebraic-geometry solutions to certain non-linear equations in terms of functions on the moduli spaces. We show that the Riemannian metrics on the moduli spaces coincide with two-point correlators in topological conformal field theory and calculate the partition function for A_n model for arbitrary genus. A universal method for constructing complete families of conservation laws for Whitham-type hierarchies of PDEs is also proposed.
%B Preprint n.117, Scuola Normale Superiore, Pisa, November 1991, 31 pp. Published in: Surveys in Differential Geometry , Vol. IV (1999), p. 213 - 238.
%I Scuola Normale Superiore di Pisa
%G en
%U http://hdl.handle.net/1963/6475
%1 6435
%2 Mathematics
%4 1
%# MAT/03 GEOMETRIA
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