Witten's conjecture and Virasoro conjecture for genus up to two

Details Witten's conjecture and Virasoro conjecture for genus up to two Witten's conjecture and Virasoro conjecture for genus up to two

2003-10-28

arxiv.org/abs/math/0310442v5

Mathematics

Algebraic Geometry

submitted to proceedings of conference "Gromov-Witten Theory of Spin Curves and Orbifolds". Final version

Scientific paper

This is an expository paper based on the results in [12] and [16]. The main
goal is to prove the following two conjectures for genus up to two.
(1) Witten's conjecture on the relations between higher spin curves and
Gelfand-Dickey Hierarchies.
(2) Virasoro conjecture for conformal semisimple Frobenius manifolds.

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