Description: |
There is (almost) no information available on the literature about complex algebraic surfaces of general type with geometric genus pg=0, self-intersection of the canonical divisor K2=3 and with 5-torsion. If S is a quintic surface in P3 having 15 3-divisible ordinary cusps as only singularities, then there is a Galois triple cover \phi:X--> S branched only at the cusps such that X is regular, pg(X)=4, KX2=15 and \phi is the canonical map of X. We use computer algebra to search for such quintics having a free action of Z5, so that X/Z5 is a smooth minimal surface of general type with pg=0 and K2=3. We find two different examples, one of them is the Van der Geer-Zagier's quintic, the other is new.
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