Virasoro constraints for Hodge integrals

2025/06/10 by Xin Wang, Wang, Xin
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2506.10033

openalex publication_date 2025/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to study Virasoro constraints for Hodge integrals in Gromov-Witten theory of any target varieties. Results consist of the following: Firstly, we propose Virasoro conjecture for Hodge integrals in Gromov-Witten theory of any target varieties; Secondly, we prove Virasoro constraints for Hodge integrals in genus zero of any target varieties; Thirdly, we prove the genus-1 L₁^𝔼 constraint with one Hodge character class insertion for any target varieties; Lastly, we obtain certain new vanishing identities in higher genus for Gromov-Witten invariants of any target varieties.

Citations

• The Virasoro-like Algebra of a Frobenius Manifold
• The Loop Equation for Special Cubic Hodge Integrals
• Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs
• On Certain Vanishing Identities For Gromov-Witten Invariants
• Genus-2 Gromov-Witten invariants for manifolds with semisimple quantum cohomology
• Idempotents on the big phase space
• Virasoro constraints for target curves
• Symplectic geometry of Frobenius structures
• Quantum Riemann - Roch, Lefschetz and Serre
• Gromov - Witten invariants and quantization of quadratic hamiltonians
• Semisimple Frobenius structures at higher genus
• The Virasoro conjecture for Gromov-Witten invariants
• Hodge integrals and Gromov-Witten theory
• Frobenius Manifolds And Virasoro Constraints
• Virasoro Constraints For Quantum Cohomology

Related

• Hodge integrals and λ_g conjecture with target varieties
• Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators
• Hodge integrals and Gromov-Witten theory
• The Virasoro conjecture for Gromov-Witten invariants
• Virasoro constraints for target curves