Meromorphic limits of automorphisms
| Autor: | Alessandro Ghigi, Leonardo Biliotti |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Mathematics - Complex Variables 010102 general mathematics Cycle space Mathematics::General Topology Automorphism 01 natural sciences Mathematics - Algebraic Geometry 0103 physical sciences FOS: Mathematics 010307 mathematical physics Geometry and Topology Compactification (mathematics) 0101 mathematics Complex manifold Complex Variables (math.CV) Algebraic Geometry (math.AG) Meromorphic function Probability measure Mathematics |
| DOI: | 10.48550/arxiv.1901.10724 |
| Popis: | Let $X$ be a compact complex manifold in the Fujiki class $\mathscr{C}$. We study the compactification of $\operatorname{Aut}^0(X)$ given by its closure in Barlet cycle space. The boundary points give rise to non-dominant meromorphic self-maps of $X$. Moreover convergence in cycle space yields convergence of the corresponding meromorphic maps. There are analogous compactifications for reductive subgroups acting trivially on $\operatorname{Alb} X$. If $X$ is K\"ahler, these compactifications are projective. Finally we give applications to the action of $\operatorname{Aut}(X)$ on the set of probability measures on $X$. In particular we obtain an extension of Furstenberg lemma to manifolds in the class $\mathscr{C}$. |
| Databáze: | OpenAIRE |
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