TY - JOUR
AU - Medina García, Nélida
PY - 2017/07/13
Y2 - 2024/08/08
TI - Ratio of varieties by actions of reductive groups
JF - Selecciones Matemáticas
JA - Sel.Mat.
VL - 4
IS - 01
SE -
DO - 10.17268/sel.mat.2017.01.03
UR - https://revistas.unitru.edu.pe/index.php/SSMM/article/view/1421
SP - 25-29
AB - 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.
ER -