| Title | Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory |
| Publication Type | Preprint |
| 1991 | |
| Authors | Dubrovin, B |
| Series Title | Preprint n.117, Scuola Normale Superiore, Pisa, November 1991, 31 pp. Published in: Surveys in Differential Geometry , Vol. IV (1999), p. 213 - 238. |
| Institution | Scuola Normale Superiore di Pisa |
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. | |
| http://hdl.handle.net/1963/6475 |
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