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Modulated semi-invariants

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.