Hodge integrals and $λ_{g}$ conjecture with target varieties
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929619539591168 |
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| author | Wang, Xin |
| author_facet | Wang, Xin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hodge integrals and $λ_{g}$ conjecture with target varieties Wang, Xin Algebraic Geometry 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. |
| title | Hodge integrals and $λ_{g}$ conjecture with target varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2412.05287 |