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arXiv:math/0110220 [math.AG]AbstractReferencesReviewsResources

Smooth, isolated curves in families of Calabi-Yau threefolds in homogeneous spaces

Andreas Leopold Knutsen

Published 2001-10-19, updated 2012-09-05Version 2

We show the existence of smooth isolated curves of different degrees and genera in Calabi-Yau threefolds that are complete intersections in homogeneous spaces. Along the way, we classify all degrees and genera of smooth curves on BN general K3 surfaces of low genera. By results of Mukai, these are the K3 surfaces that can be realised as complete intersections in certain homogeneous spaces.

Comments: 18 pages. The previous version of the preprint used a result from a published paper that turned out to have a gap. The gap has been fixed in another paper, so finally the results of this preprint have a complete proof. Moreover, the whole preprint has been rewritten, with some simplified proofs
Categories: math.AG
Subjects: 14J32, 14J28
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