Work

Proper triangular 𝔾a-actions on 𝔸4are translations

Year: 2014

Type: article

Abstract: We describe the structure of geometric quotients for proper locally triangulable ‫އ‬ a -actions on locally trivial ‫ށ‬ 3 -bundles over a nœtherian normal base scheme X defined over a field of characteristic 0. In the case where dim X = 1, we show in particular that every such action is a translation with geometric quotient isomorphic to the total space of a vector bundle of rank 2 over X .As a consequence, every proper triangulable ‫އ‬ a -action on the affine four space ‫ށ‬ 4 k over a field of characteristic 0 is a translation with geometric quotient isomorphic to ‫ށ‬ 3 k .

Source: Algebra & Number Theory

DOI: 10.2140/ant.2014.8.1959

Authors: Adrien Dubouloz, David Finston, Imad Jaradat

Institutions: Centre National de la Recherche Scientifique, Université de Bourgogne, Institut de Mathématiques de Bourgogne, New Mexico State University, Jordan University of Science and Technology

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Agence Nationale de la Recherche, Office of International Science and Engineering

Awards: Polynomial Automorphisms and Birational Transformations, U.S.-France Planning Visit: Cancellation Problems