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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds


Author: Andreas Leopold Knutsen
Journal: Trans. Amer. Math. Soc. 364 (2012), 5243-5264
MSC (2010): Primary 14D15; Secondary 14B05, 14C05, 14C20, 14H45, 14J28, 14J32, 14N10
Published electronically: May 22, 2012
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Abstract: Building on results of Clemens and Kley, we find criteria for a continuous family of curves in a nodal $ K$-trivial threefold $ Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation $ Y_t$ of $ Y_0$. As an application, we show the existence of smooth isolated curves of bounded genera and unbounded degrees in Calabi-Yau complete intersection threefolds.


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Additional Information

Andreas Leopold Knutsen
Affiliation: Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway
Email: andreas.knutsen@math.uib.no

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05461-4
PII: S 0002-9947(2012)05461-4
Keywords: Isolated curves, deformations, Hilbert schemes, Calabi-Yau threefolds, singularities
Received by editor(s): January 14, 2010
Received by editor(s) in revised form: April 19, 2010, June 8, 2010, and September 4, 2010
Published electronically: May 22, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.