Positivity of extensions of vector bundles
Algebraic Geometry
2023-12-18 v2
Abstract
In this paper, we study when positivity conditions of vector bundles are preserved by extension. We prove that an extension of a big (resp. pseudo-effective) line bundle by an ample (resp. a nef) vector bundle is big (resp. pseudo-effective). We also show that an extension of an ample line bundle by a big line bundle is not necessarily pseudo-effective. In particular, this implies that an almost nef vector bundle is not necessarily pseudo-effective.
Keywords
Cite
@article{arxiv.2307.05022,
title = {Positivity of extensions of vector bundles},
author = {Sho Ejiri and Osamu Fujino and Masataka Iwai},
journal= {arXiv preprint arXiv:2307.05022},
year = {2023}
}
Comments
v2: 8 pages, completely revised version, to appear in Mathematische Zeitschrift. v1: 7 pages, comments are welcome