Beauville surface

In mathematics, a Beauville surface is one of the surfaces of general type introduced by Arnaud Beauville (1996, exercise X.13 (4)).

Let C1 and C2 be smooth curves with genera g1 and g2.

Let G be a finite group acting on C1 and C2 such that Then the quotient (C1 × C2)/G is a Beauville surface.

One example is to take C1 and C2 both copies of the genus 6 quintic X5 + Y5 + Z5 =0, and G to be an elementary abelian group of order 25, with suitable actions on the two curves.

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