On subvarieties with ample normal bundle

  • John Christian Ottem

    University of Oslo, Norway


We show that a pseudoeffective R\mathbb R-divisor has numerical dimension 0 if it is numerically trivial on a subvariety with ample normal bundle. This implies that the cycle class of a curve with ample normal bundle is big, which gives an affirmative answer to a conjecture of Peternell. We also give other positivity properties of such subvarieties.

Cite this article

John Christian Ottem, On subvarieties with ample normal bundle. J. Eur. Math. Soc. 18 (2016), no. 11, pp. 2459–2468

DOI 10.4171/JEMS/644