POSITIVITY PROPERTIES OF TORIC VECTOR BUNDLES

Milena Hering, Mircea Mustata, Sam Payne

Research output: Contribution to journalArticlepeer-review

Abstract

We show that a torus-equivariant vector bundle on a complete tonic variety is nef or ample if and only if its restriction to every invariant curve is nef or ample, respectively. Furthermore, we show that nef tonic vector bundles have a nonvanishing global section at every point and deduce that the underlying vector bundle is trivial if and only if its restriction to every invariant curve is trivial. We apply our methods and results to study, in particular, the vector bundles M-L that arise as the kernel of the evaluation map H-0 (X, L) circle times O-X -> L, for ample line bundles L. We give examples of twists of such bundles that are ample but not globally generated.

Original languageEnglish
Pages (from-to)607-640
Number of pages34
JournalAnnales de l'Institut Fourier
Volume60
Issue number2
DOIs
Publication statusPublished - 2010

Fingerprint

Dive into the research topics of 'POSITIVITY PROPERTIES OF TORIC VECTOR BUNDLES'. Together they form a unique fingerprint.

Cite this