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Rigid Curves in Complete Intersection Calabi–Yau Threefolds

Published online by Cambridge University Press:  04 December 2007

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

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.

Type
Research Article
Copyright
© 2000 Kluwer Academic Publishers

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