Quasi-modular forms from mixed Noether-Lefschetz theory - FAKKIR

Quasi-modular forms from mixed Noether-Lefschetz theory

FAKKIR.XYZ | JURNAL – The Gromov-Witten theory of three folds admitting a smooth K3 fibration can be solved in terms of the Noether-Lefschetz intersection numbers of the fibration and the reduced invariants of a K3 surface. Toward a generalization of this result to families with singular fibers, we introduce completed Noether Lefschetz numbers using toroidal compactifications of the period space of elliptic K3 surfaces. As an application, we prove quasi-modularity for some genus 0 partition functions of Weierstrass fibrations over ruled surfaces, and show that they satisfy a holomorphic anomaly equation.

 

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