Rigid curves in complete intersection Calabi-Yau threefolds
نویسنده
چکیده
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. Mathematics Subject Classifications (1991): 14C05, 14J32 (Primary); 14C25, 14H52, 14J28 (Secondary).
منابع مشابه
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We give a criterion for a continuous family of curves on a nodal Ktrivial threefold X0 to contribute geometrically rigid curves to a general smoothing of X0. As an application, we prove the existence of geometrically rigid curves of arbitrary degree and explicitly bounded genus on general complete intersection Calabi-Yau threefolds. Mathematics Subject Classifications (1991): 14C05, 14J32 (Prim...
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