JournalsggdVol. 5, No. 1pp. 107–119

On Beauville surfaces

  • Yolanda Fuertes

    Universidad Autónoma de Madrid, Spain
  • Gabino González-Diez

    Universidad Autónoma de Madrid, Spain
  • Andrei Jaikin-Zapirain

    Universidad Autónoma de Madrid, Spain
On Beauville surfaces cover
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Abstract

We prove that if a finite group GG acts freely on a product of two curves C1×C2C_1 \times C_2 so that the quotient S=C1×C2/GS=C_1 \times C_2/G is a Beauville surface then C1C_1 and C2C_2 are both non hyperelliptic curves of genus 6\geq 6; the lowest bound being achieved when C1=C2C_1 = C_2 is the Fermat curve of genus 66 and G=(Z/5Z)2G=\left(\mathbb{Z}/5\mathbb{Z} \right)^2. We also determine the possible values of the genera of C1C_1 and C2C_2 when GG equals S5S_5, PSL2(F7)\mathrm{PSL}_2(\mathbb{F}_7) or any abelian group. Finally, we produce examples of Beauville surfaces in which GG is a pp-group with p=2,3p=2,3.

Cite this article

Yolanda Fuertes, Gabino González-Diez, Andrei Jaikin-Zapirain, On Beauville surfaces. Groups Geom. Dyn. 5 (2011), no. 1, pp. 107–119

DOI 10.4171/GGD/117