English

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