Isolated rational curves on K3-fibered Calabi–Yau threefolds

被引：0

作者：

Torsten Ekedahl

Trygve Johnsen

Dag Einar Sommervoll

机构：

[1] Department of Mathematics,

[2] Stockholm University,undefined

[3] S-106 91 Stockholm,undefined

[4] ¶Sweden. e-mail: teke@matematik.su.se,undefined

[5] Department of Mathematics,undefined

[6] University of Bergen,undefined

[7] N-5008 Bergen,undefined

[8] Norway. e-mail:johnsen@mi.uib.no,undefined

[9] Statistics Norway,undefined

[10] N-0033 Oslo,undefined

[11] Norway. e-mail: des@ssb.no,undefined

来源：

manuscripta mathematica | 1999年 / 99卷

关键词：

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

D O I：

暂无

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学科分类号：

摘要：

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.

引用

页码：111 / 133

页数：22