Surfaces with p_{g}=q=2 and an irrational pencil
We classify all the irrational pencils over the surfaces of general type with p=q=2. This classification adds a new evidence to a Catanese conjecture which states that if S has p=q=2 but no irrational pencils then it is the double cover of a P.P. Abelian variety branched on a reduced divisor linearly equivalent to twice a theta divisor.
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