  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.
