Semipositivity theorems for moduli problems

By O. Fujino. 2012

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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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0efecd38544ee7dfc2dec2382754d546720e53f7

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

K-stability of Fano varieties: an algebro-geometric approach (2020, methodology): “he argument in [LX14] for Ding invariants, and conclude that Ding stability and K-stability are indeed the same for Fano varieties. A key technical advantage for Ding invariant, observed by Fujita in [Fuj18], is that we can deﬁne Ding(F) more generally for a linearly bounded multiplicative ﬁltration”
Fundamental theorems for semi log canonical pairs (2012, methodology): “moduli spaces of stable pairs. By combining the arguments in the proof of Theorem 1.2 with our new semi-positivity theorem in [FF] (see also [FFS]), we obtain the following semi-positivity theorem in [F16]. Theorem 1.21 (see [F16, Theorem 1.8]). Let X be an equidimensional variety which satisﬁes Ser”