Vertex and source determine the block variety of an indecomposable module 
David J. Benson and Markus Linckelmann

Abstract.
  
The block variety $V_{G,b}(M)$ of a finitely generated 
indecomposable module $M$ over the block
algebra of a $p$-block $b$ of a finite group $G$, introduced in [\Linc], 
can be computed in terms of a vertex and a source of $M$.
We use this to show that $V_{G,b}(M)$ is connected, and that every closed
homogeneous subvariety of the affine variety $V_{G,b}$ defined by block
cohomology $H^*(G,b)$ (cf.\ [\Linb]) is the variety of a module 
over the block algebra. This is analogous to the corresponding
statements on Carlson's cohomology varieties in [\Cac].