Positivity of extensions of vector bundles

Sho Ejiri; Osamu Fujino; Masataka Iwai

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arXiv · 2307.05022

Positivity of extensions of vector bundles

Sho Ejiri·Osamu Fujino·Masataka Iwai

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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.

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Sho Ejiri, Osamu Fujino, Masataka Iwai. 2023-07-11. Positivity of extensions of vector bundles. https://arxiv.org/abs/2307.05022

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