Invariant curves for birational surface maps

Diller, Jeffrey; Jackson, Daniel; Sommese, Andrew

doi:10.1090/S0002-9947-07-04162-1

Invariant curves for birational surface maps
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by Jeffrey Diller, Daniel Jackson and Andrew Sommese PDF

Trans. Amer. Math. Soc. 359 (2007), 2973-2991 Request permission

Abstract:

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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