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math.AG2017★ 24 cited
Gromov-Witten theory of elliptic fibrations: Jacobi forms and holomorphic anomaly equations
Georg Oberdieck, Aaron Pixton
We conjecture that the relative Gromov-Witten potentials of elliptic fibrations are (cycle-valued) lattice quasi-Jacobi forms and satisfy a holomorphic anomaly equation. We prove t…
math.AG2017★ 52 cited
Holomorphic anomaly equations and the Igusa cusp form conjecture
Georg Oberdieck, Aaron Pixton
Let be a K3 surface and let be an elliptic curve. We solve the reduced Gromov-Witten theory of the Calabi-Yau threefold for all curve classes which are primiti…