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No abstract

Given a foliation F in an algebraic surface having a rational first integral a genus formula for the general solution is obtained. In the case S = P 2 some new counterexamples to the classic formulation of the Poincaré problem are presented. If S is a rational surface and F has singularities of type (1, 1) or (1, −1) we prove that the general solution is a non-singular curve.

We rewrite in modern language a classical construction by W. E. Edge showing a pencil of sextic nodal curves admitting A5 as its group of automorphism. Next, we discuss some other aspects of this pencil, such as the associated fibration and its connection to the singularities of the moduli of six-dimensional abelian varieties.