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- W4386044143 abstract "Let $pi : X to B$ be an elliptically fibered threefold satisfying $c_3(T_X otimes omega_X)=0$. We conjecture that the $pi$-relative generating series of Pandharipande-Thomas invariants of $X$ are quasi-Jacobi forms and satisfy two holomorphic anomaly equations. For elliptic Calabi-Yau threefolds our conjectures specialize to the Huang-Katz-Klemm conjecture. The proposed formulas constitute the first case of holomorphic anomaly equations in Pandharipande-Thomas theory. We prove our conjectures for the equivariant Pandharipande-Thomas theory of $mathbb{C}^2 times E$ when specialized to the anti-diagonal action. For $K3 times mathbb{C}$ we state reduced versions of our conjectures. As a corollary we find an explicit conjectural formula for the stationary theory generalizing the Katz-Klemm-Vafa formula for K3 surfaces. Further evidence is available for $mathbb{P}^2 times E$ based on earlier work of the second author. To deal with elliptic threefolds with $c_3(T_X otimes omega_X) neq 0$ we show that the moduli space of $pi$-stable pairs is represented by a proper algebraic space. We conjecture that the associated $pi$-stable pair invariants form quasi-Jacobi forms." @default.
- W4386044143 created "2023-08-22" @default.
- W4386044143 creator A5014684784 @default.
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- W4386044143 date "2023-08-18" @default.
- W4386044143 modified "2023-09-26" @default.
- W4386044143 title "Pandharipande-Thomas theory of elliptic threefolds, quasi-Jacobi forms and holomorphic anomaly equations" @default.
- W4386044143 doi "https://doi.org/10.48550/arxiv.2308.09652" @default.
- W4386044143 hasPublicationYear "2023" @default.
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