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arXiv · 2412.05287

Hodge integrals and $\lambda_{g}$ conjecture with target varieties

Xin Wang
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Abstract

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

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Xin Wang. 2024-11-21. Hodge integrals and $\lambda_{g}$ conjecture with target varieties. https://arxiv.org/abs/2412.05287

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