Nef vector bundles on a projective space with first Chern class three

Abstract

We classify nef vector bundles on a projective space with first Chern class three over an algebraically closed field of characteristic zero; we see, in particular, that these nef vector bundles are globally generated if the second Chern class is less than eight, and that there exist nef but non-globally generated vector bundles with second Chern class eight and nine on a projective plane.

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Correspondence to Masahiro Ohno.

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This work was partially supported by JSPS KAKENHI (C) Grant Number 15K04810.

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Ohno, M. Nef vector bundles on a projective space with first Chern class three. Rend. Circ. Mat. Palermo, II. Ser 69, 425–458 (2020). https://doi.org/10.1007/s12215-019-00412-5

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Keywords

  • Nef vector bundles
  • Fano bundles
  • Spectral sequences

Mathematics Subject Classification

  • 14J60
  • 14F05