Date: Wednesday, March 08, 2017
Location: 4096 East Hall (4:10 PM to 5:30 PM)
Title: Positivity of cotangent bundles of manifolds with pseudoeffective canonical class
Abstract: Given a projective manifold, one can measure the positive directions in its tangent bundle by evaluating the slopes of its subsheaves with respect to movable classes. We show that the holomorphic foliations with positive slope and stable with respect to a movable class are algebraic. As a consequence, we infer that any quotient of an arbitrary tensor power of the cotangent bundle of the manifold has a pseudoeffective determinant, provided that the canonical class of the manifold is pseudoeffective. This represents a generalization of the celebrated generic semipositivity theorem by Y. Miyaoka. A few other applications will be discussed. These results are part of a joint work with F. Campana.
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Speaker: Mihai Paun
Institution: University of Illinois, Chicago
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