On the Picard group of a compact complex nilmanifold. II (Q1091525)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the Picard group of a compact complex nilmanifold. II |
scientific article; zbMATH DE number 4010933
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Picard group of a compact complex nilmanifold. II |
scientific article; zbMATH DE number 4010933 |
Statements
On the Picard group of a compact complex nilmanifold. II (English)
0 references
1987
0 references
[For part I of this paper see ibid. 13, 631-638 (1983; Zbl 0542.14032)]. This paper deals with the compact complex nilmanifolds \(X=(G/\Gamma)\) of which the Albanese torus T is isogenous to a product of elliptic curves. It is proved that: 1) the Albanese map \(\pi\) : \(X\to T\) has holomorphic sections. 2) \(\pi^*(Pic(T))\) has finite index in Pic(X). The main tool is Malcev basis for \(\Gamma\) in G. Some explicit examples are treated, including the Iwasawa manifold.
0 references
Picard group
0 references
compact complex nilmanifolds
0 references
Albanese torus
0 references
Malcev basis
0 references
