d-elliptic Loci in Genus 2 and 3-Reference-Cited by-同舟云学术

d-elliptic Loci in Genus 2 and 3

Published:2020-12-14 Issue:20 Volume:2021 Page:15959-16007
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Lian Carl¹

Affiliation:

1. Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, 12489, Germany

Abstract

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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/20/15959/40740032/rnaa303.pdf

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1. Correction to: d-elliptic loci in genus 2 and 3;International Mathematics Research Notices;2024-01-30

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