The algebraic density property for affine toric varieties

Kutzschebauch, Frank; Leuenberger, Matthias; Liendo Rojas, Alvaro Patricio (2015). The algebraic density property for affine toric varieties. Journal of pure and applied algebra, 219(8), pp. 3685-3700. North-Holland 10.1016/j.jpaa.2014.12.017

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In this paper we generalize the algebraic density property to not necessarily smooth affine varieties relative to some closed subvariety containing the singular locus. This property implies the remarkable approximation results for holomorphic automorphisms of the Andersén–Lempert theory. We show that an affine toric variety X satisfies this algebraic density property relative to a closed T-invariant subvariety Y if and only if X∖Y≠TX∖Y≠T. For toric surfaces we are able to classify those which possess a strong version of the algebraic density property (relative to the singular locus). The main ingredient in this classification is our proof of an equivariant version of Brunella's famous classification of complete algebraic vector fields in the affine plane.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Kutzschebauch, Frank; Leuenberger, Matthias and Liendo Rojas, Alvaro Patricio

Subjects:

500 Science > 510 Mathematics

ISSN:

0022-4049

Publisher:

North-Holland

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

24 Jun 2016 10:05

Last Modified:

18 Dec 2016 02:30

Publisher DOI:

10.1016/j.jpaa.2014.12.017

ArXiv ID:

1402.2227v2

BORIS DOI:

10.7892/boris.82550

URI:

https://boris.unibe.ch/id/eprint/82550

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