On the normal bundles of rational curves on Fano 3-folds

A component of very free rational curves on a variety is called unbalanced if the normal bundle of a general member is unbalanced. In this paper we show that all components of very free rational curves on a Fano threefold of Picard number one are balanced with the only exception being the space of conics on $\mathbb{P}^3$.

Keywords

Rational curves, Fano threefolds

2010 Mathematics Subject Classification

14D15, 14M22

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Published 6 April 2012