On the existence of curves in K-trivial threefolds

1998/11/17 by Holger P. Kley, Kley, Holger P.
Mathematics · #14C05 #14C25 #14J28 (Secondary #14J32 (Primary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C05 #msc:14C25 #msc:14J28 #msc:14J32

paper · pdf · doi:10.48550/arxiv.math/9811099

8 pages, LaTeX2e

arxiv created 1998/11/17 · arxiv updated 2009/11/30

Abstract

We give a criterion for a continuous family of curves on a nodal K-trivial 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.

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