We prove that if a finite group G acts freely on a product of two curves C1×C2 so that the quotient S=C1×C2/G is a Beauville surface then C1 and C2 are both non hyperelliptic curves of genus ≥6; the lowest bound being achieved when C1=C2 is the Fermat curve of genus 6 and G=(Z/5Z)2. We also determine the possible values of the genera of C1 and C2 when G equals S5, PSL2(F7) or any abelian group. Finally, we produce examples of Beauville surfaces in which G is a p-group with p=2,3.
Yolanda Fuertes; Gabino González-Diez; Andrei Jaikin-Zapirain. On Beauville surfaces. Groups, geometry, and dynamics, Tome 5 (2011) no. 1, pp. 107-119. doi: 10.4171/ggd/117
@article{10_4171_ggd_117,
author = {Yolanda Fuertes and Gabino Gonz\'alez-Diez and Andrei Jaikin-Zapirain},
title = {On {Beauville} surfaces},
journal = {Groups, geometry, and dynamics},
pages = {107--119},
year = {2011},
volume = {5},
number = {1},
doi = {10.4171/ggd/117},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/117/}
}
TY - JOUR
AU - Yolanda Fuertes
AU - Gabino González-Diez
AU - Andrei Jaikin-Zapirain
TI - On Beauville surfaces
JO - Groups, geometry, and dynamics
PY - 2011
SP - 107
EP - 119
VL - 5
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/117/
DO - 10.4171/ggd/117
ID - 10_4171_ggd_117
ER -
