manuscripta mathematica

, Volume 99, Issue 1, pp 111–133

Isolated rational curves on K3-fibered Calabi–Yau threefolds

  • Torsten Ekedahl
  • Trygve Johnsen
  • Dag Einar Sommervoll

DOI: 10.1007/s002290050165

Cite this article as:
Ekedahl, T., Johnsen, T. & Sommervoll, D. manuscripta math. (1999) 99: 111. doi:10.1007/s002290050165

Abstract:

In this paper we study 16 complete intersection K3-fibered Calabi--Yau variety types in biprojective space ℙn1}×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.

Mathematics Subject Classification (1991):Primary 14J30; Secondary 14J28, 14H45 

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Torsten Ekedahl
    • 1
  • Trygve Johnsen
    • 2
  • Dag Einar Sommervoll
    • 3
  1. 1.Department of Mathematics, Stockholm University, S-106 91 Stockholm,¶Sweden. e-mail: teke@matematik.su.seSE
  2. 2.Department of Mathematics, University of Bergen, N-5008 Bergen, Norway. e-mail:johnsen@mi.uib.noNO
  3. 3.Statistics Norway, N-0033 Oslo, Norway. e-mail: des@ssb.noNO

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