Modular forms from Noether–Lefschetz
theory

Greer, François

doi:10.2140/ant.2020.14.2335

Alg. Number Th.

2020

DOI: 10.2140/ant.2020.14.2335

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Modular forms from Noether–Lefschetz theory

François Greer

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Quasi-modular forms from mixed Noether-Lefschetz theory

Greer¹

2019

Advances in Mathematics

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The Gromov-Witten theory of threefolds 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. Sketch of a programAn old approach to computing Gromov-Witten invariants on X is to embed ι : X ֒→ P as a complete intersection in a more positive variety P , often with a torus action. Composing with ι induces an embedding of Kontsevich spaces M g (X, β) ֒→ M g (P, ι * β).

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Quasi-modular forms from mixed Noether-Lefschetz theory

Greer¹

2019

Advances in Mathematics

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Modular forms from Noether–Lefschetz theory

Cited by 1 publication

References 19 publications

Quasi-modular forms from mixed Noether-Lefschetz theory

Quasi-modular forms from mixed Noether-Lefschetz theory

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