Journal of the European Mathematical Society


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Volume 18, Issue 11, 2016, pp. 2459–2468
DOI: 10.4171/JEMS/644

Published online: 2016-10-12

On subvarieties with ample normal bundle

John Christian Ottem[1]

(1) University of Oslo, Norway

We show that a pseudoeffective $\mathbb R$-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.

Keywords: Ample normal bundles, Hartshorne’s conjecture, positive cycles

Ottem John Christian: On subvarieties with ample normal bundle. J. Eur. Math. Soc. 18 (2016), 2459-2468. doi: 10.4171/JEMS/644