Hodge integrals and λ_g conjecture with target varieties

2024/11/21 by Xin Wang, Wang, Xin
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2412.05287

openalex publication_date 2024/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose λ_g conjecture for Hodge integrals with target varieties. Then we establish relations between Virasoro conjecture and λ_g conjecture, in particular, we prove λ_g conjecture in all genus for smooth projective varieties with semisimple quantum cohomology or smooth algebraic curves. Meanwhile, we also prove λ_g conjecture in genus zero for any smooth projective varieties. In the end, together with DR formula for λ_g class, we obtain a new type of universal constraints for descendant Gromov-Witten invariants. As an application, we prove λ_g conjecture in genus one for any smooth projective varieties.

Related

• Virasoro constraints for Hodge integrals
• Hodge integrals and Gromov-Witten theory
• Hodge integrals, partition matrices, and the lambda_g conjecture
• Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators
• A Survey of the Hodge Conjecture for Abelian Varieties