Rational surface maps with invariant meromorphic two-forms
J Diller, JL Lin - Mathematische Annalen, 2016 - Springer
J Diller, JL Lin
Mathematische Annalen, 2016•SpringerLet f: S\dashrightarrow S f: S⤏ S be a rational self-map of a smooth complex projective
surface SS and η η be a meromorphic two-form on SS satisfying f^* η= δ η f∗ η= δ η for
some δ ∈ C^* δ∈ C∗. We show that under a mild topological assumption on ff, there is a
birational change of domain ψ: X\dashrightarrow S ψ: X⤏ S such that ψ^* η ψ∗ η has no
zeros. In this context, we investigate the notion of algebraic stability for ff, proving that ff can
be made algebraically stable if and only if it acts nicely on the poles of η η. We illustrate this …
surface SS and η η be a meromorphic two-form on SS satisfying f^* η= δ η f∗ η= δ η for
some δ ∈ C^* δ∈ C∗. We show that under a mild topological assumption on ff, there is a
birational change of domain ψ: X\dashrightarrow S ψ: X⤏ S such that ψ^* η ψ∗ η has no
zeros. In this context, we investigate the notion of algebraic stability for ff, proving that ff can
be made algebraically stable if and only if it acts nicely on the poles of η η. We illustrate this …
Abstract
Let be a rational self-map of a smooth complex projective surface and be a meromorphic two-form on satisfying for some . We show that under a mild topological assumption on , there is a birational change of domain such that has no zeros. In this context, we investigate the notion of algebraic stability for , proving that can be made algebraically stable if and only if it acts nicely on the poles of . We illustrate this last result in the case , where we translate our stability result into a condition on whether a circle homeomorphism associated to has rational rotation number.
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