Negative answers to some positivity questions
Massachusetts Institute of Technology. Department of Mathematics.
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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.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.47Cataloged from PDF version of thesis.Includes bibliographical references (pages 61-64).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology