Existence of sections of line bundles over a toroidal group and its applications
type: Item
instance of: scholarly article
title: Existence of sections of line bundles over a toroidal group and its applications
zbMATH Open document ID: 0808.32027
DOI: 10.1007/BF02572345
author: Yukitaka Abe
published in: Mathematische Zeitschrift
publication date: 1995-03-15T00:00:00Z
full work available at URL: https://eudml.org/doc/174674
review text: We consider the existence problem of sections of line bundles over a toroidal group. We give a partial answer in the general case, from which we can obtain a Lefschetz type theorem. Let \(R(X,L)\) be the graded ring associated to a line bundle \(L\) over a toroidal group \(X\). We also prove that the transcendence degree of the field of the homogeneous fractions of degree zero of \(R(X,L)\) is infinite if \(L\) has a positive definite hermitian form. Furthermore, the equalities of the Kodaira dimension, the numerical rank and the rank are proved.
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 32G20
zbMATH DE Number: 703851
zbMATH Keywords: existence
zbMATH Keywords: sections of line bundles
zbMATH Keywords: toroidal group
MaRDI profile type: Publication
cites work: (H, C)-groups with positive line bundles
cites work: On toroidal groups
cites work: Q4734098
cites work: On periodic functions of several complex variables. II: Reduction to the positive definite case
cites work: Periodic meromorphic functions
cites work: Q3864183
cites work: Q5735265
cites work: Two remarks concerning toroidal groups
OpenAlex ID: W2078866036
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description: scientific article; zbMATH DE number 703851