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2010•arXiv (Cornell University)Open access

On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds

Andreas Leopold Knutsen

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Abstract

Building on results of Clemens and Kley, we find criteria for a continuous family of curves in a nodal $K$-trivial threefold $Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation $Y_t$ of $Y_0$. 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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What this paper is about

Building on results of Clemens and Kley, we find criteria for a continuous family of curves in a nodal $K$-trivial threefold $Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation $Y_t$ of $Y_0$. 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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Available abstract

Building on results of Clemens and Kley, we find criteria for a continuous family of curves in a nodal $K$-trivial threefold $Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation $Y_t$ of $Y_0$. As an application, we show the existence of smooth isolated curves of bounded genera and unbounded degrees in Calabi-Yau complete intersections threefolds.

Key concepts: Calabi–Yau manifold, Intersection (aeronautics), Bounded function, Mathematics, Pure mathematics, Complete intersection, Scheme (mathematics), Mathematical analysis

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