Abstract
Inspired by constructions of automorphisms on rational surfaces and a recent paper of Perroni and Zhang (Mathematische Annalen 359(1–2):189–209, 2014), we give a concrete construction of pseudoautomorphisms of higher dimensional rational surfaces that have an invariant cuspidal curve and first dynamical degree larger than one. Taking advantage of the group structure on the smooth points of the curve and elementary projective geometry, we arrive at explicit formulas for these pseudoautomorphisms. Though it is not used in our construction, we further indicate a relationship between aspects of our construction with certain coxeter groups.
1991 Mathematics Subject Classification. 14E07, 32H04, 37F99
The first and second authors are grateful for support from the National Science Foundation
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Bedford, E., Diller, J., Kim, K. (2015). Pseudoautomorphisms with Invariant Curves. In: Fornæss, J., Irgens, M., Wold, E. (eds) Complex Geometry and Dynamics. Abel Symposia, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-20337-9_1
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DOI: https://doi.org/10.1007/978-3-319-20337-9_1
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