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arXiv · 2604.05664

The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds

Reginald Anderson·Dominic Joyce
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Abstract

Let $X$ be a projective complex 3-manifold. An effective curve class $\beta\in H_2(X,\mathbb Z)$ is called positive if $c_1(X)\cdot\beta>0$, and superpositive if all the effective summands of $\beta$ 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.

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Reginald Anderson, Dominic Joyce. 2026-04-07. The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds. https://arxiv.org/abs/2604.05664

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