This paper is a continuation of hepth/0507224 where open topological B-models
describing D-branes on 2-cycles of local Calabi--Yau geometries with conical
singularities were studied. After a short review, the paper expands in
particular on two aspects: the gauge fixing problem in the reduction to two
dimensions and the quantum matrix model solutions.Comment: 17 p. To appear in proc. Symposium QTS-4, Varna (Bulgaria), August
200
