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arXiv · 2004.06768

d-elliptic loci in genus 2 and 3

Carl Lian
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Abstract

We consider the loci of curves of genus 2 and 3 admitting a $d$-to-1 map to a genus 1 curve. After compactifying these loci via admissible covers, we obtain formulas for their Chow classes, recovering results of Faber-Pagani and van Zelm when $d=2$. The answers exhibit quasimodularity properties similar to those in the Gromov-Witten theory of a fixed genus 1 curve; we conjecture that the quasimodularity persists in higher genus, and indicate a number of possible variants.

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Carl Lian. 2020-04-14. d-elliptic loci in genus 2 and 3. https://arxiv.org/abs/2004.06768

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