Non-Kahler complex structures on R4, II

被引：2

作者：

Di Scala, Antonio J. ^{[1
]}

Kasuya, Naohiko ^{[2
]}

Zuddas, Daniele ^{[3
]}

机构：

[1] Politecn Torino, Dipartimento Sci Matemat GL Lagrange, Corso Duca Abruzzi 24, I-10129 Turin, Italy

[2] Kyoto Sangyo Univ, Dept Math, Kita Ku, Kyoto 6038555, Japan

[3] Univ Bayreuth, Math Inst, Lehrstuhl Math 8, NW 2,Univ Str 30, D-95447 Bayreuth, Germany

来源：

JOURNAL OF SYMPLECTIC GEOMETRY | 2018年 / 16卷 / 03期

关键词：

SURFACES;

D O I：

10.4310/JSG.2018.v16.n3.a2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We follow our study of non-Kahler complex structures on R-4 that we defined in our previous paper. We prove that these complex surfaces do not admit any smooth complex compactification. Moreover, we give an explicit description of their meromorphic functions. We also prove that the Picard groups of these complex surfaces are uncountable, and give an explicit description of the canonical bundle. Finally, we show that any connected non-compact oriented 4-manifold admits complex structures without Kahler metrics.

引用

页码：631 / 644

页数：14

共 22 条

[1]

[Anonymous], 1967, Topology, DOI 10.1016/0040-9383(67)90034-1

[2] Lefschetz fibrations over the disc [J].

Apostolakis, Nikos ;

Piergallini, Riccardo ;

Zuddas, Daniele .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2013, 107 :340-390

[3] A CLASS OF COMPACT, COMPLEX MANIFOLDS WHICH ARE NOT ALGEBRAIC [J].

CALABI, E ;

ECKMANN, B .

ANNALS OF MATHEMATICS, 1953, 58 (03) :494-500

[4] ON ANALYTIC SURFACES WITH 2 INDEPENDENT MEROMORPHIC FUNCTIONS [J].

CHOW, WL ;

KODAIRA, K .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1952, 38 (04) :319-325

[5] Non-Kahler complex structures on R4 [J].

Di Scala, Antonio J. ;

Kasuya, Naohiko ;

Zuddas, Daniele .

GEOMETRY & TOPOLOGY, 2017, 21 (04) :2461-2473

[6] On embeddings of almost complex manifolds in almost complex Euclidean spaces [J].

Di Scala, Antonio J. ;

Kasuya, Naohiko ;

Zuddas, Daniele .

JOURNAL OF GEOMETRY AND PHYSICS, 2016, 101 :19-26

[7] COMPLEX SUBMANIFOLDS OF ALMOST COMPLEX EUCLIDEAN SPACES [J].

Di Scala, Antonio J. ;

Vezzoni, Luigi .

QUARTERLY JOURNAL OF MATHEMATICS, 2010, 61 (04) :401-405

[8] ON SURFACES OF CLASS-VII0 WITH CURVES [J].

ENOKI, I .

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1980, 56 (06) :275-279

[9]

Gompf R., 1999, 4-manifolds and Kirby calculus, V20o

[10]

Gompf R.E., 1997, GEOM TOPOL, V1, P41

← 1 2 3 →