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

Preprint

Let X be a projective complex 3-manifold. An effective curve class β∈H2(X,ℤ) is called positive if c1(X)⋅β>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.

Authors: Anderson, R; Joyce, D

• Publication status: Published
• Peer review status: Not peer reviewed
• Preprint server: arXiv
• Publication date: 2026-04-07
• DOI: 10.48550/arXiv.2604.05664
• EISSN: 2331-8422
• Language: English