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Rigid Curves in Complete Intersection Calabi–Yau Threefolds

Published online by Cambridge University Press:  04 December 2007

Holger P. Kley
Holger P. Kley
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, U.S.A. E-mail: kley@math.utah.edu
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Abstract

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Working over the complex numbers, we study curves lying in a complete intersection K3 surface contained in a (nodal) complete intersection Calabi–Yau threefold. Under certain generality assumptions, we show that the linear system of curves in the surface is a connected componend of the the Hilbert scheme of the threefold. In the case of genus one, we deduce the existence of infinitesimally rigid embeddings of elliptic curves of arbitrary degree in the general complete intersection Calabi–Yau threefold.

Keywords

Calabi–Yau threefoldsHilbert schemesK3 surfaces
Type
Research Article
Information
Compositio Mathematica , Volume 123 , Issue 2 , September 2000 , pp. 185 - 208
Copyright
© 2000 Kluwer Academic Publishers