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

2003/11/07 by Y.-P. Lee, Y. -P. Lee, Lee, Y. -P. · 5 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AG #math.SG

paper · pdf · doi:10.48550/arxiv.math/0311100

openalex publication_date 2003/11/07 · arxiv created 2004/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants

Cited by

• Invariance of tautological equations I: conjectures and applications
• Towards a description of the double ramification hierarchy for Witten's r-spin class
• BCOV's Feynman rule of quintic 3-folds
• An algebraic scheme associated with the non-commutative KP hierarchy and some of its extensions
• N=1 formal genus zero Gromov–Witten theories and Givental’s formalism

Related

• Witten's conjecture and Virasoro conjecture for genus up to two
• Tautological relations via r-spin structures
• Tautological equations in genus 2 via invariance conjectures
• Invariance of tautological equations II: Gromov--Witten theory
• The Virasoro conjecture for Gromov-Witten invariants