Ratio of varieties by actions of reductive groups
DOI:
https://doi.org/10.17268/sel.mat.2017.01.03Keywords:
Varieties, small groupsAbstract
We consider the ring of polynomials R = K[x1, dots, xn] in the variables x1, dots, xn and complex coefficients. The permutation group of 1, dots, n acts sore R by permuting the variables. The set of invariants by this action forms a ring generated by elementary symmetric polynomials. Emmy Noether proves that if a finite group of inverse matrices G subsetGL(n; k) acts on R, then the ring of invariants is generated by a finite number of invariant homogeneous and defines an operator in G to obtain invariant polynomials. There are algebraic relationships between the generators of the invariant ring and the orbits of Cn/G. In 1963, Masayoshi Nagata demonstrated that the ring of the invariants of geomagically reductive groups is finitely generated. We analice the existence of a quotient variety X/G where G is an algebraic group acting on an algebraic variety X.References
Cox David, Little Jhon & O'shea Donald. Ideals, Varieties, and Algorithms, Tercera edición, Springer Science-Business Media, USA.2007.
Fléischmann Peter. On Invariant Theory of Finite Groups, Institut of Mathematics and Statistics. University of Kent at Canterbury. 2006.
Reynoso Claudia. Introducción a la Teoría de Invariantes Geométricos, Departamento de Guanajuato, Guanajuato, México. 2010.
Published
How to Cite
Issue
Section
License
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.
