Birational geometry of irregular varieties in zero and positive characteristic

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Title Birational geometry of irregular varieties in zero and positive characteristic
Publication Type dissertation
School or College College of Science
Department Mathematics
Author Wang, Yuan
Date 2017
Description In this dissertation, we mainly focus on constructing two results that characterize cer- tain varieties by their birational invariants. In characteristic 0, we generalize a celebrated theorem of Kawamata by showing that for a projective log canonical pair (X, ∆), if the Kodaira dimension of KX + ∆ is 0 and the dimension of the Albanese variety Alb(X) of X is equal to the dimension of X, then X is birational to an abelian variety. In characteristic p > 0, we show a classification result for surfaces of general type beyond the Noether line. More precisely, suppose that S is a minimal projective surface in characteristic p ≥ 11, χ(OS) = 1 and dim(Alb(S)) = 4, and S lifts to the second Witt vectors. Then under mild assumption on the Albanese variety and the Albanese morphism of S, S is a product of two smooth curves of genus 2.
Type Text
Publisher University of Utah
Subject Pure sciences; Birational geometry; Irregular varieties; Zero and positive characteristic
Dissertation Name Doctor of Philosophy
Language eng
Rights Management ©Yuan Wang
Format application/pdf
Format Medium application/pdf
ARK ark:/87278/s6wm5jr5
Setname ir_etd
ID 1347734
Reference URL https://collections.lib.utah.edu/ark:/87278/s6wm5jr5
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