d-elliptic loci in genus 2 and 3
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866929216217415680 |
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| author | Lian, Carl |
| author_facet | Lian, Carl |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_06768 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | d-elliptic loci in genus 2 and 3 Lian, Carl Algebraic Geometry 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. |
| title | d-elliptic loci in genus 2 and 3 |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2004.06768 |