Abstract:
In this paper we study 16 complete intersection K3-fibered Calabi--Yau variety types in biprojective space ℙn 1}×ℙ1. These are all the CICY-types that are K3 fibered by the projection on the second factor. We prove existence of isolated rational curves of bidegree (d,0) for every positive integer d on a general Calabi–Yau variety of these types. The proof depends heavily on existence theorems for curves on K3-surfaces proved by S. Mori and K. Oguiso. Some of these varieties are related to Calabi–Yau varieties in projective space by a determinantal contraction, and we use this to prove existence of rational curves of every degree for a general Calabi–Yau variety in projective space.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 14 October 1997 / Revised version: 18 January 1998
Rights and permissions
About this article
Cite this article
Ekedahl, T., Johnsen, T. & Sommervoll, D. Isolated rational curves on K3-fibered Calabi–Yau threefolds. manuscripta math. 99, 111–133 (1999). https://doi.org/10.1007/s002290050165
Issue Date:
DOI: https://doi.org/10.1007/s002290050165