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

MathSciNet review:
2931328

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Abstract: Building on results of Clemens and Kley, we find criteria for a continuous family of curves in a nodal -trivial threefold to deform to a scheme of finitely many smooth isolated curves in a general deformation of . 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:
https://doi.org/10.1090/S0002-9947-2012-05461-4

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.