Quotient Spaces Modulo Algebraic Groups

Quotient Spaces modulo Algebraic Groups

In algebraic geometry one often encounters the problem of taking the quotient of a scheme by a group. Despite the frequent occurrence of such problems, there are few general results about the existence of such quotients. These questions come up again and again in the theory of moduli spaces. When we want to classify some type of algebraic objects, say varieties or vector bundles, the classifica...

Projective normality of quotient varieties modulo finite groups

In this note, we prove that for any finite dimensional vector space V over an algebraically closed field k, and for any finite subgroup G of GL(V ) which is either solvable or is generated by pseudo reflections such that the |G| is a unit in k, the projective variety P(V )/G is projectively normal with respect to the descent of O(1)⊗|G|.

Some topological properties of quotients modulo semisimple algebraic groups

We will prove a general result in Invariant Theory, viz. for a quotientC==G, whereG is a connected complex semisimple algebraic group, the local first homology group at any point in the quotient C==G is trivial and the local second homology group is finite. Using this we will prove that the completion of the local ring of any point in C==G is a unique factorization domain (UFD). Mathematics Sub...

Algebraic distance in algebraic cone metric spaces and its properties

In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.

ε-weakly Chebyshev subspaces and quotient spaces