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2020 Modular forms from Noether–Lefschetz theory
François Greer
Algebra Number Theory 14(9): 2335-2368 (2020). DOI: 10.2140/ant.2020.14.2335

Abstract

We enumerate smooth rational curves on very general Weierstrass fibrations over hypersurfaces in projective space. The generating functions for these numbers lie in the ring of classical modular forms. The method of proof uses topological intersection products on a period stack and the cohomological theta correspondence of Kudla and Millson for special cycles on a locally symmetric space of orthogonal type. The results here apply only in base degree 1, but heuristics for higher base degree match predictions from the topological string partition function.

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François Greer. "Modular forms from Noether–Lefschetz theory." Algebra Number Theory 14 (9) 2335 - 2368, 2020. https://doi.org/10.2140/ant.2020.14.2335

Information

Received: 31 January 2019; Revised: 27 March 2020; Accepted: 29 April 2020; Published: 2020
First available in Project Euclid: 12 November 2020

MathSciNet: MR4172710
Digital Object Identifier: 10.2140/ant.2020.14.2335

Subjects:
Primary: 14NXX

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 9 • 2020
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