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.

The quotient of an algebraic variety by action of an algebraic group does not always has a variety structure. The aim of this work is to describe a methodfor constructing good quotients, in the sense of Geometric invariant theory, in algebraicgeometry.

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.

The quotient of an algebraic variety by action of an algebraic group does not always has a variety structure. The aim of this work is to describe a methodfor constructing good quotients, in the sense of Geometric invariant theory, in algebraicgeometry.

The objectives of this workshop are: 1). Train participants in the handling of Input Bar, Views, Spreadsheet, Options menu, Slider, Text, Scroll graphical view, Intersection, Perpendicular and some commands of the GeoGebra Classic 5 program; 2). Facilitate significant learning of the formal concept of limit of a real function at a number and at infinity and, 3). Develop the ability to communicate and represent mathematical ideaswith limit of real functions. Development: We explore the GeoGebra Views, tools and commands that we will use. We present an Activity that contains the intuitive and formal definitions of limit of a real function at a number and at infinity, examples on limit of functions to solve and questions oriented to the intuitive concept and later to a dynamic construction of the formal concept of limit, with GeoGebra support. We proceed in a similar way with the concept li...