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Invariant curves for birational surface maps


Authors: Jeffrey Diller, Daniel Jackson and Andrew Sommese
Journal: Trans. Amer. Math. Soc. 359 (2007), 2973-2991
MSC (2000): Primary 32H50, 14E07, 14H45
DOI: https://doi.org/10.1090/S0002-9947-07-04162-1
Published electronically: January 4, 2007
MathSciNet review: 2286065
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Jeffrey Diller
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: diller.1@nd.edu

Daniel Jackson
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Address at time of publication: Department of Mathematics and Computer Science, University of Maine at Farmington, 117 South Street, Farmington, Maine 04938
Email: djackso1@nd.edu, daniel.jackson1@maine.edu

Andrew Sommese
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: sommese@nd.edu

DOI: https://doi.org/10.1090/S0002-9947-07-04162-1
Keywords: Birational map, complex dynamics, invariant curve
Received by editor(s): May 1, 2005
Received by editor(s) in revised form: July 21, 2005
Published electronically: January 4, 2007
Additional Notes: During preparation of this paper, the third author was supported by National Science Foundation grant DMS-0410047, and the first and second authors were supported by grant DMS 0140408.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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