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

摘要

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.