Log canonical models of foliated surfaces
Yen-An Chen
TL;DR
This paper investigates the properties of log canonical models of foliated surfaces of general type, establishing boundedness, valuative criteria, and invariance of plurigenera, contributing to the understanding of their moduli spaces.
Contribution
It introduces new boundedness results for log canonical models of foliated surfaces and analyzes their moduli functor, including criteria for separatedness and properness.
Findings
Log canonical models of general type are bounded.
Valuative criteria of separatedness and properness are established.
Invariance of plurigenera for foliated surfaces is proved.
Abstract
We study log canonical models of foliated surfaces of general type. In particular, we show that log canonical models of general type and their minimal partial du Val resolutions are bounded. Moreover, we show the valuative criteria of separatedness and properness and a property related to local-closedness for the moduli functor which parametrizes the stable smoothable foliated surface pairs. On the way, we also show a result on the invariance of plurigenera.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology