Explicit formulas for infinitely many Shimura curves in genus 4

Samuel Grushevsky; Martin Moeller

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arXiv · 1510.05674

Explicit formulas for infinitely many Shimura curves in genus 4

Samuel Grushevsky·Martin Moeller

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Abstract

In this paper we construct infinitely many Shimura curves contained in the locus of Jacobians of genus four curves. All Jacobians in these families are ${\mathbb Z}/3$ covers of varying elliptic curves that appear in a geometric construction of Pirola, and include an example of a Shimura-Teichmuller curve that parameterizes Jacobians that are suitable ${\mathbb Z}/6$ covers of ${\mathbb P}^1$. We compute explicitly the period matrices of the Shimura curves we construct using the original construction of Shimura for moduli spaces of abelian varieties with automorphisms.

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BibTeX RIS

Samuel Grushevsky, Martin Moeller. 2015-10-19. Explicit formulas for infinitely many Shimura curves in genus 4. https://arxiv.org/abs/1510.05674

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