d-elliptic loci and quasi-modular forms

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• Carl Lian, Tufts University.
• Wednesday 14 May 2025, 14:15-15:15
• CMS MR13.

If you have a question about this talk, please contact Dhruv Ranganathan.

Let N_{g,d} be the locus of curves of genus g admitting a degree d cover of an elliptic curve. For fixed g, it is conjectured that the classes of N_{g,d} on M_g are the Fourier coefficients of a cycle-valued quasi-modular form in d. A key difficulty is that these classes are often non-tautological, so lie outside the reach of many known techniques. Via the Torelli map, the conjecture can be moved to one on certain Noether-Lefschetz loci on A_g, where there is accesss to different tools. I will explain some evidence for these conjectures, gathered from results of many people, some of which are joint with François Greer and Naomi Sweeting.

This talk is part of the Algebraic Geometry Seminar series.

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