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

Abstract

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.