Negative answers to some positivity questions
Name
890211399-MIT.pdf
Description
Full printable version
Size
3.31 MB
Format
Adobe PDF
Checksum (MD5)
cf2dda29ae432ad9a8347250a2c4f0be
Author(s)
Lesieutre, John
Advisor(s)
James McKernan.
Date Issued
2014
Publisher
Massachusetts Institute of Technology
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.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
47
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 61-64).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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