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The main purpose of this article is to define the notion of Du Bois singularities for pairs and proving a vanishing theorem using this new notion. The main vanishing theorem specializes to a new vanis...
We use Cox's description for sheaves on toric varieties and results about the local cohomology with respect to monomial ideals to give a characteristic free approach to vanishing results on arbitrary...
We extend our family rigidity and vanishing theorems in [{\bf LiuMaZ}] to the Spin^c case. In particular, we prove a K-theory version of the main results of [{\bf H}], [{\bf Liu1}, Theorem B] for a fa...