Witten's conjecture, Virasoro conjecture, and invariance of tautological equations

Details Witten's conjecture, Virasoro conjecture, and invariance of tautological equations Witten's conjecture, Virasoro conjecture, and invariance of tautological equations

2003-11-07

arxiv.org/abs/math/0311100v2

Mathematics

Algebraic Geometry

Scientific paper

The main goal of this paper 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 hierarchy. 2. Virasoro conjecture for target manifolds with conformal semisimple Frobenius manifolds. The main technique used in the proof is the invariance of tautological equations under loop group action.

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