Variedades de representações de quivers

Abstract

One of the main problems of quiver representation theory is to classify all the indecomposable representations for a given quiver $Q$. There is an approach to this problem via algebraic geometry that turned out to be useful for some wild-type path algebras, known for its difficulty. Motivated by this, we study the main object of this approach, called the variety of representations of quivers. In order to understand the scope of this concept, we explore an example of each type of algebra, namely finite, tame and wild types. In other words, we study its generic classification of its indecomposable representations via orbit classification. In order to study the tangent space of these varieties and their orbits, we study some homological tools and its main properties.