  We prove the basic properties of determinantal semi-invariants for
presentation spaces over any finite dimensional hereditary algebra over any
field. These include the virtual generic decomposition theorem, stability
theorem and the c-vector theorem which says that the c-vectors of a cluster
tilting object are, up to sign, the determinantal weights of the determinantal
semi-invariants defined on the cluster tilting objects. Applications of these
theorems are given in several concurrently written papers.
