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.References
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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
- 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.
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2286065