On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds
Abstract
Building on results of Clemens and Kley, we find criteria for a continuous family of curves in a nodal K-trivial threefold Y0 to deform to a scheme of finitely many smooth isolated curves in a general deformation Yt of Y0. As an application, we show the existence of smooth isolated curves of bounded genera and unbounded degrees in Calabi-Yau complete intersections threefolds.
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