Tautness and Fatou Components in P^2
Han Peters, Crystal Zeager
TL;DR
This paper studies the tautness of invariant Fatou components in holomorphic endomorphisms of P^2, revealing new tautness results for recurrent components and establishing Kobayashi completeness for certain cases.
Contribution
It extends the understanding of tautness in Fatou components beyond basins of attraction, identifying new taut recurrent components and proving Kobayashi completeness.
Findings
Recurrent Fatou components are taut.
Basin of attraction components are taut.
Certain Fatou components are Kobayashi complete.
Abstract
We investigate the tautness of invariant Fatou components for holomorphic endomorphisms of P^2. Previously, only basins of attraction were known to be taut. We show that two other kinds of recurrent Fatou components are taut. In the first of these cases, as well as for basins of attraction, we show that the Fatou components are in fact Kobayashi complete, which implies tautness.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory