Nef vector bundles on a projective space or a hyperquadric with the first Chern class small

Abstract

We give a new proof of the classification due to Peternell-Szurek-Wiśniewski of nef vector bundles on a projective space with the first Chern class less than three and on a smooth hyperquadric with the first Chern class less than two over an algebraically closed field of characteristic zero.

29 pages; v3: The title is changed, and sections 2 and 3 in v2 are simplified and unified; v2: An error in Remark 7.6 is fixed, and the corresponding corrections are made in Theorem 7.5. Lemmas 7.2 and 7.4 are improved and Lemma 7.4 becomes Theorem 7.4. Some proofs are replaced by shorter ones