Infinitesimal semi‐invariant pictures and co‐amalgamation

Abstract

The purpose of this paper is to study the local structure of the semi‐invariant picture of a tame hereditary algebra near the null root. Using a construction that we call co‐amalgamation, we show that this local structure is completely described by the semi‐invariant pictures of a collection of self‐injective Nakayama algebras. We then describe the cones of this local structure using cluster‐like structures that we call support regular clusters. Finally, we show that the local structure is (piecewise linearly) invariant under cluster tilting.