Negative answers to some positivity questions

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2014

Author dc:creator

• Lesieutre, John

Advisor dc:contributor.advisor

• James McKernan.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/90187

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/90187