Invariant curves for birational surface maps

Details Invariant curves for birational surface maps Invariant curves for birational surface maps

2005-05-01

arxiv.org/abs/math/0505014v1

Mathematics

Algebraic Geometry

18 Pages

Scientific paper

We classify invariant curves for birational surface maps that are expanding on cohomology. When the expansion is exponential, the arithmetic genus of an invariant curve is at most one. This implies severe constraints on both the type and number of irreducible components of the curve. In the case of an invariant curve with genus equal to one, we show that there is an associated invariant meromorphic two form.

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