On the Normal Bundle of Submanifolds of P

  title={On the Normal Bundle of Submanifolds of P},
  author={Lucian B Adescu},
  • Lucian B Adescu
  • Published 2007
Let X be a submanifold of dimension d ≥ 2 of the complex projec-tive space P n. We prove results of the following type. i) If X is irregular and n = 2d then the normal bundle N X|P n is indecomposable. ii) If X is irregular, d ≥ 3 and n = 2d+1 then N X|P n is not the direct sum of two vector bundles of rank ≥ 2. iii) If d ≥ 3, n = 2d − 1 and N X|P n is decomposable then the natural restriction map Pic(P n) → Pic(X) is an isomorphism (and in particular, if X = P d−1 × P 1 embedded Segre in P 2d… CONTINUE READING