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Deformations and cohomology of minimal varieties
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Deformations and cohomology of minimal varieties
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Dissertation
Deformations and cohomology of minimal varieties
1997
Overview
Mori's theory of extremal rays and minimal models has breathed new life into the classification problem in algebraic geometry. In this thesis, we investigate the behavior of minimal varieties under deformation. First, we show the preservation of minimality under an arbitrary smooth, projective deformation. Then, using results of Kodaira, Horikawa, Mori, and Kollar, we deduce the deformation invariance of plurigenera under small projective deformations. Along the way, we establish the basepoint free theorem for smooth minimal varieties, and discuss briefly the problem of computing bounds for effective non-vanishing. Lastly, we also make conjectures for both Kahler varieties and higher dimensional varieties, based on the results for both surfaces and three-folds.
