Configurations and Galleries varieties
DOI link for Configurations and Galleries varieties
Configurations and Galleries varieties book
This chapter introduces the Configuration varieties defined by typical graphs. The galleries of types, or more generally the linear typical graphs, define a class of k-smooth and integral Configurations varieties particularly important in this work. A minimal generalized gallery of the Flag Complex is a general point of the Configurations variety given by its gallery of types. The configurations variety associated to the graph is a smooth resolution of singularities such that the pull-back of the tangent submodule admits an extension as a locally trivial submodule. The generalized gallery may be completed into an adapted gallery so that: as it follows from some equalities. Thus one has necessarily that length, and that is a minimal gallery. It is concluded that for all maximal length flag , at maximal distance from d, the generalized gallery is minimal.