Universität zu Köln

Kraft, Hanspeter, Regeta, Andriy and van Santen, Immanuel (2021). Is the Affine Space Determined by Its Automorphism Group? Int. Math. Res. Notices, 2021 (6). S. 4280 - 4301. OXFORD: OXFORD UNIV PRESS. ISSN 1687-0247

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Abstract

In this note we study the problem of characterizing the complex affine space An via its automorphism group. We prove the following. Let X be an irreducible quasi-projective n-dimensional variety such that Aut(X) and Aut(A(n)) are isomorphic as abstract groups. If X is either quasi-affine and toric or X is smooth with Euler characteristic chi(X) not equal 0 and finite Picard group Pic(X), then X is isomorphic to A(n). The main ingredient is the following result. Let X be a smooth irreducible quasiprojective variety of dimension n with finite Pic(X). If X admits a faithful (Z/pZ)(n)-action for a prime p and chi(X) is not divisible by p, then the identity component of the centralizer Cent(Aut(X))((Z/pZ)(n)) is a torus.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kraft, Hanspeter UNSPECIFIED UNSPECIFIED UNSPECIFIED Regeta, Andriy UNSPECIFIED UNSPECIFIED UNSPECIFIED van Santen, Immanuel UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-573975
DOI:	10.1093/imrn/rny281
Journal or Publication Title:	Int. Math. Res. Notices
Volume:	2021
Number:	6
Page Range:	S. 4280 - 4301
Date:	2021
Publisher:	OXFORD UNIV PRESS
Place of Publication:	OXFORD
ISSN:	1687-0247
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/57397