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

Knutsen, Andreas

doi:10.1090/S0002-9947-2012-05461-4

On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds
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by Andreas Leopold Knutsen PDF

Trans. Amer. Math. Soc. 364 (2012), 5243-5264 Request permission

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 intersection threefolds.

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