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arXiv:1010.2002 [math.AG]AbstractReferencesReviewsResources

Lengths of chains of minimal rational curves on Fano manifolds

Kiwamu Watanabe

Published 2010-10-11Version 1

In this paper, we consider a natural question how many minimal rational curves are needed to join two general points on a Fano manifold X of Picard number 1. In particular, we study the minimal length of such chains in the cases where the dimension of X is at most 5, the coindex of X is at most 3 and X equips with a structure of a double cover. As an application, we give a better bound on the degree of Fano 5-folds of Picard number 1.

Comments: 16 pages. To appear in Journal of Algebra
Journal: Journal of Algebra Volume 325, Issue 1, 1 January 2011, Pages 163-176
Categories: math.AG
Subjects: 14E30, 14J45, 14N99
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