Semipositivity theorems for moduli problems

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 Kollár. This completes Kollár's projectivity criterion for the moduli spaces of higher-dimensional stable varieties.

19 pages, v2: very minor revision, v3: major revisions, v4: revision following referee's report, v5: very minor modifications

References in corpus (2)

• Moduli of varieties of general type
• Hulls and Husks

Cited by in corpus (10)

• On semipositivity, injectivity and vanishing theorems
• Quasi-projectivity of the moduli space of smooth Kahler-Einstein Fano manifolds
• Projectivity of the moduli space of stable log-varieties and subadditvity of log-Kodaira dimension
• Cone theorem and Mori hyperbolicity
• PL density invariant for type II degenerating K3 surfaces, Moduli compactification and hyperKahler metrics
• Some remarks on the semi-positivity theorems
• Ampleness of the CM line bundle on the moduli space of canonically polarized varieties
• Polystable log Calabi-Yau varieties and Gravitational instantons
• Vanishing and semipositivity theorems for semi-log canonical pairs
• Weak positivity theorem and Frobenius stable canonical rings of geometric generic fibers