Positivity of extensions of vector bundles

2023/07/11 by Ejiri, Sho, Fujino, Osamu, Iwai, Masataka
#14F06 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14J60 #Secondary 14E99

paper · doi:10.48550/arxiv.2307.05022

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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