Tohoku Mathematical Journal
2018
September
SECOND SERIES VOL. 70, NO. 3

Tohoku Math. J.
70 (2018), 401-423

Title ON THE RATIONAL COHOMOLOGY OF REGULAR SURFACES ISOGENOUS TO A PRODUCT OF CURVES WITH $\CHI(\MATHCAL{O}_S)=2$

Author Matteo A. Bonfanti

(Received December 7, 2015, revised March 1, 2016)
Abstract. Let $S$ be a surface isogenous to a product of curves of unmixed type. After presenting several results useful to study the cohomology of $S$ we prove a structure theorem for the cohomology of regular surfaces isogenous to a product of unmixed type with $\chi (\mathcal{O}_S)=2$. In particular we found two families of surfaces of general type with maximal Picard number.

Mathematics Subject Classification. Primary 14J29; Secondary 14C22.
Key words and phrases. Surfaces isogenous to a product of curves, Picard number.

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