Generic vanishing, pluri-canonical maps and volume of isolated sigularity

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Title Generic vanishing, pluri-canonical maps and volume of isolated sigularity
Publication Type dissertation
School or College College of Science
Department Mathematics
Author Zhang, Yuchen
Date 2014-05
Description In this thesis, we consider two different problems in birational geometry considered previously in the author's papers. The first problem concerns pluri-canonical maps in positive characteristic. We prove that for a smooth variety X of general type over an algebraically closed field k with positive characteristic, if X has maximal Albanese dimension and the Albanese map is separable, then |4KX| induces a birational map. The second problem is on the volume of isolated singularities over C. We give an equivalent definition of the local volume of an isolated singularity VolBdFF(X, 0) defined by Boucksom, de Fernex and Favre in the Q-Gorenstein case and we generalize it to the non-Q-Gorenstein case. We prove that there is a positive lower bound depending only on the dimension for the non-zero local volume of an isolated singularity if X is Gorenstein. We also give a non-Q-Gorenstein example with VolBdFF(X, 0) = 0, which does not allow a boundary such that the pair (X, ) is log canonical.
Type Text
Publisher University of Utah
Subject Pluri-canonical maps; Isolated singularity
Dissertation Institution University of Utah
Dissertation Name Doctor of Philosophy
Language eng
Rights Management Copyright © Yuchen Zhang 2014
Format application/pdf
Format Medium application/pdf
Format Extent 361,689 Bytes
Identifier etd3/id/2868
ARK ark:/87278/s6477k2r
Setname ir_etd
ID 196436
Reference URL https://collections.lib.utah.edu/ark:/87278/s6477k2r
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