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 (J. Algebra 215 (1999) 460), can be computed in terms of a vertex and a source of M. We use this to show that VG,b(M) is connected, and that every closed homogeneous subvariety of the affine variety VG.b defined by block cohomology H*(G, b) (cf. Al.-ebras Rep. Theory 2 (1999) 107) is the variety of a module over the block algebra. This is analogous to the corresponding statements on Carlson's cohomology varieties in (lnvent. Math. 77 (1984) 291). © 2004 Elsevier B.V. All rights reserved.
- source algebras