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In mathematics, a Beauville surface is one of the surfaces of general type introduced by Arnaud Beauville ( 1996, exercise X.13 (4)). They are examples of "fake quadrics", with the same Betti numbers as quadric surfaces.
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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