Weak positivity theorem and Frobenius stable canonical rings of geometric generic fibers

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• Sho Ejiri (Tokyo)
• Monday 23 November 2015, 16:30-17:30
• CMS MR4.

If you have a question about this talk, please contact Caucher Birkar.

In characteristic zero, Fujita, Kawamata, Viehweg, Fujino and many others showed semi positivity theorems and weak positivity theorems which are important re- sults on the positivity of direct images of relative pluricanonical bundles. However, in positive characteristic, there are counter-examples to these theorems. In this talk, we show that an analogue of weak positivity theorems holds in positive characteristic, when the canonical ring of the geometric generic fiber F is finitely generated and the Frobenius stable canonical ring of F is large enough.

This talk is part of the Algebraic Geometry Seminar series.

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