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

Andreas Leopold Knutsen

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

Algebraic Geometry 2010-09-23 v1

Authors: Andreas Leopold Knutsen

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.

Keywords

calabi-yau threefold isolated smooth curves complete intersection k-trivial threefold deformation theory

Cite

@article{arxiv.1009.4419,
  title  = {On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds},
  author = {Andreas Leopold Knutsen},
  journal= {arXiv preprint arXiv:1009.4419},
  year   = {2010}
}

Comments

22 pages, to appear in Transactions of the AMS

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

Abstract

Keywords

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