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.

引用

页码：663 / 675

页数：13

共 26 条

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[2]

[Anonymous], 1986, ADV SER MATH PHYS, V1, P145

[3]

Barth W. P., 2004, CORNPACT COMPLEX SUR, V4

[4]

Campana F, 2004, ANN I FOURIER, V54, P499, DOI 10.5802/aif.2027