Semipositivity theorems for moduli problems
Osamu Fujino
TL;DR
This paper establishes semipositivity theorems for singular varieties derived from mixed Hodge structures, leading to a proof of Kollár's projectivity criterion for moduli spaces of higher-dimensional stable varieties.
Contribution
It proves new semipositivity theorems for singular varieties and completes Kollár's projectivity criterion for moduli spaces of higher-dimensional stable varieties.
Findings
Semipositivity theorems for singular varieties from mixed Hodge structures
Moduli functor of stable varieties is semipositive
Completion of Kollár's projectivity criterion
Abstract
We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the sense of Koll\'ar. This completes Koll\'ar's projectivity criterion for the moduli spaces of higher-dimensional stable varieties.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology