Beauville surface

In mathematics, a Beauville surface is one of the surfaces of general type introduced by . They are examples of "fake quadrics", with the same Betti numbers as quadric surfaces.
Construction.
Let "C"1 and "C"2 be smooth curves with genera "g"1 and "g"2.
Let "G" be a finite group acting on "C"1 and "C"2 such that
Then the quotient ("C"1 × "C"2)/"G" is a Beauville surface.
One example is to take "C"1 and "C"2 both copies of the genus 6 quintic
"X"5 + "Y"5 + "Z"5 =0, and "G" to be an elementary abelian group of order 25, with suitable actions on the two curves.
Invariants.
Hodge diamond: