Infinite generation for rings of symmetric tensors
type: Item
instance of: scholarly article
title: Infinite generation for rings of symmetric tensors
zbMATH Open document ID: 0839.53048
published in: Mathematical Research Letters
publication date: 1995-01-01T00:00:00Z
review text: M. Gromov has introduced a Kähler hyperbolic manifold as Kähler manifold \((X, \omega)\) with its universal cover \(\widetilde {X}\) such that the pullback of \(\omega\) can be written as \(d\alpha\), where \(\alpha\) is a 1-form bounded in the \(L_\infty\)-norm with respect to the induced Kähler metric on \(\widetilde {X}\). Let \(\Delta\) be the unit disc and \(X\) an irreducible compact quotient of \(\Delta\times \Delta\). The author proves that \(X\) is Kähler hyperbolic and the algebra \(\bigoplus_{n\geq 0} H^0 (X, \text{Symm}^n \Omega^1_X)\) of holomorphic symmetric tensors on \(X\) is not finitely generated.
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 817741
zbMATH Keywords: Kähler hyperbolic space
zbMATH Keywords: divisor class
zbMATH Keywords: Chern class
zbMATH Keywords: holomorphic symmetric tensors
author: N. I. Shepherd-Barron
reviewed by: Neda Bokan
MaRDI profile type: Publication
full work available at URL: mrl.1995.v2.n2.a2
OpenAlex ID: W2320554841
DOI: 10.4310/MRL.1995.V2.N2.A2
description: scientific article; zbMATH DE number 817741