RATIONAL CURVES ON FIBERED CALABI-YAU MANIFOLDS

被引：0
|
作者：
Diverio, Simone [1 ]
Fontanari, Claudio [2 ]
Martinelli, Diletta [3 ]
机构：
[1] Sapienza Univ Roma, Dipartimento Matemat Guido Castelnuovo, Piazzale Aldo Moro 5, I-00185 Rome, Italy
[2] Univ Trento, Dipartimento Matemat, Via Sommarive 14, I-38123 Povo, Trento, Italy
[3] Univ Edinburgh, Sch Math, Peter Guthrie Tait Rd, Edinburgh SW7 2AZ, Midlothian, Scotland
来源：
DOCUMENTA MATHEMATICA | 2019年 / 24卷
关键词：
Elliptic fiber space; Calabi-Yau manifold; fibration; rational curve; rational multi-section; canonical bundle formula; THREEFOLDS; CONJECTURE;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that a smooth projective complex manifold of dimension greater than two endowed with an elliptic fiber space structure and with finite fundamental group always contains a rational curve, provided its canonical bundle is relatively trivial. As an application of this result, we prove that any Calabi-Yau manifold that admits a fibration onto a curve whose general fiber is an abelian variety always contains a rational curve.
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页码：663 / 675
页数：13
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