TY - RPRT
T1 - Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory
Y1 - 1991
A1 - Boris Dubrovin
AB - 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.
JF - Preprint n.117, Scuola Normale Superiore, Pisa, November 1991, 31 pp. Published in: Surveys in Differential Geometry , Vol. IV (1999), p. 213 - 238.
PB - Scuola Normale Superiore di Pisa
UR - http://hdl.handle.net/1963/6475
U1 - 6435
U2 - Mathematics
U4 - 1
U5 - MAT/03 GEOMETRIA
ER -