## Involve: A Journal of Mathematics

• Involve
• Volume 9, Number 4 (2016), 639-655.

### Jacobian varieties of Hurwitz curves with automorphism group $\mathrm{PSL}(2,q)$

#### Abstract

The size of the automorphism group of a compact Riemann surface of genus $g > 1$ is bounded by $84(g − 1)$. Curves with automorphism group of size equal to this bound are called Hurwitz curves. In many cases the automorphism group of these curves is the projective special linear group $PSL(2,q)$. We present a decomposition of the Jacobian varieties for all curves of this type and prove that no such Jacobian variety is simple.

#### Article information

Source
Involve, Volume 9, Number 4 (2016), 639-655.

Dates
Revised: 8 July 2015
Accepted: 20 July 2015
First available in Project Euclid: 22 November 2017

https://projecteuclid.org/euclid.involve/1511371048

Digital Object Identifier
doi:10.2140/involve.2016.9.639

Mathematical Reviews number (MathSciNet)
MR3530204

Zentralblatt MATH identifier
1345.14038

#### Citation

Fischer, Allison; Liu, Mouchen; Paulhus, Jennifer. Jacobian varieties of Hurwitz curves with automorphism group $\mathrm{PSL}(2,q)$. Involve 9 (2016), no. 4, 639--655. doi:10.2140/involve.2016.9.639. https://projecteuclid.org/euclid.involve/1511371048

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