Structures in topological recursion relations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910003599769600 |
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| author | Janda, Felix Wang, Xin |
| author_facet | Janda, Felix Wang, Xin |
| contents | In this paper, we study the basic structures of degree-$g$ topological recursion relations on the moduli space of curves $\overline{\mathcal{M}}_{g,n}$: (i) The coefficient of the bouquet class on $\overline{\mathcal{M}}_{g,n}$, which gives the answer to a conjecture of T. Kimura and X. Liu; (ii) Linear relations among the coefficients of certain rational tails locus of $\overline{\mathcal{M}}_{g,n}$.
Three applications of topological recursion relations will be discussed: (i) Coefficients of universal equations for Gromov-Witten invariants for any smooth projective variety; (ii) The coefficient of the bouquet class in the double ramification formula of the top Hodge class $λ_g$; (iii) A new recursive formula for computing the intersection numbers on the moduli space of stable curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20673 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Structures in topological recursion relations Janda, Felix Wang, Xin Algebraic Geometry 14N35 (Primary) 14N10 (Secondary) In this paper, we study the basic structures of degree-$g$ topological recursion relations on the moduli space of curves $\overline{\mathcal{M}}_{g,n}$: (i) The coefficient of the bouquet class on $\overline{\mathcal{M}}_{g,n}$, which gives the answer to a conjecture of T. Kimura and X. Liu; (ii) Linear relations among the coefficients of certain rational tails locus of $\overline{\mathcal{M}}_{g,n}$. Three applications of topological recursion relations will be discussed: (i) Coefficients of universal equations for Gromov-Witten invariants for any smooth projective variety; (ii) The coefficient of the bouquet class in the double ramification formula of the top Hodge class $λ_g$; (iii) A new recursive formula for computing the intersection numbers on the moduli space of stable curves. |
| title | Structures in topological recursion relations |
| topic | Algebraic Geometry 14N35 (Primary) 14N10 (Secondary) |
| url | https://arxiv.org/abs/2601.20673 |