Pandharipande-Thomas theory of elliptic threefolds, quasi-Jacobi forms and holomorphic anomaly equations

Georg Oberdieck, Maximilian Schimpf

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…