The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915920416342016 |
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| author | Anderson, Reginald Joyce, Dominic |
| author_facet | Anderson, Reginald Joyce, Dominic |
| contents | Let $X$ be a projective complex 3-manifold. An effective curve class $β\in H_2(X,\mathbb Z)$ is called positive if $c_1(X)\cdotβ>0$, and superpositive if all the effective summands of $β$ are positive. If $X$ is Fano then all curve classes are superpositive. In arXiv:2111.04694 the second author developed a theory of enumerative invariants in abelian categories and wall-crossing formulae. We use this theory to prove conjectures by Pandharipande and Thomas on the rationality and poles of generating functions of Pandharipande-Thomas invariants of $X$ with descendent insertions, for superpositive curve classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05664 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds Anderson, Reginald Joyce, Dominic Algebraic Geometry Let $X$ be a projective complex 3-manifold. An effective curve class $β\in H_2(X,\mathbb Z)$ is called positive if $c_1(X)\cdotβ>0$, and superpositive if all the effective summands of $β$ are positive. If $X$ is Fano then all curve classes are superpositive. In arXiv:2111.04694 the second author developed a theory of enumerative invariants in abelian categories and wall-crossing formulae. We use this theory to prove conjectures by Pandharipande and Thomas on the rationality and poles of generating functions of Pandharipande-Thomas invariants of $X$ with descendent insertions, for superpositive curve classes. |
| title | The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.05664 |