Invariant curves for birational surface maps
By Jeffrey Diller, D. Jackson, Andrew J. Sommese. 2005
48 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a75559f91dd63cec34c693c727f08c435c037557
How researchers see this paper
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In Geometry and Topology
- Serge Cantat
- Jeffrey Diller
- Kyounghee Kim
- Eric Bedford
- J. Blanc
- John Lesieutre
- Takato Uehara
- Keiji Oguiso
In Mathematical Physics
- Serge Cantat
- Jeffrey Diller
- Kyounghee Kim
- Eric Bedford
- J. Blanc
- John Lesieutre
- Takato Uehara
- Keiji Oguiso
Citations in the corpus
- Dynamics of automorphisms of compact complex surfaces (2014, background): “The genus of E can be defined in terms of the genus formula g(E) = E · (E + KX)/2+1, where KX is the canonical class of X ; it coincides with 1−χ(OC), where χ denotes the Euler characteristic (see [53]).”
- Dynamics of Rational Surface Automorphisms: Linear Fractional Recurrences (2006, background): “2 of [11] since q is indeterminate for f −1.”
- Cremona transformations, surface automorphisms and plane cubics (2008, background): “It is a consequence of results in [ DJS ] that if f : P 2 → P 2 is a quadratic transformation properly fixing a curve C, then deg C ≤ 3, with equality if and only if I(f), I(f −1 ) ⊂ C.”