Title: Negative Answers To Some Positivity Questions
Abstract: We construct counterexamples to a number of
questions related to positivity properties of line bundles on
algebraic varieties. The examples are based on studying the
geometry of varieties that admit pseudo automorphisms of positive
entropy, and in particular on the action of standard Cremona
transformations on blow-ups of projective space at configurations
of points. The main examples include the following: nefness is not
an open condition in families; the diminished base locus of a
divisor is not always a closed set; Zariski decompositions do not
necessarily exist in dimension three; asymptotic multiplicity
invariants are not always finite in the relative setting; and the
number of Fourier- Mukai partners of a variety can be
infinite.
Publication Year: 2014
Publication Date: 2014-01-01
Language: en
Type: dissertation
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