Modulated semi-invariants

Abstract

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.

41 pages, 1 figure, many minor changes, c-vector theorem redone

References in corpus (1)

• Periodic trees and semi-invariants

Cited by in corpus (10)

• Signed exceptional sequences and the cluster morphism category
• A survey on maximal green sequences
• Linearity of stability conditions
• Cambrian frameworks for cluster algebras of affine type
• The No Gap Conjecture for tame hereditary algebras
• The formula for the permutation of mutation sequences in $A_n$ straight orientation
• Maximal green sequences of quivers with multiple edges
• Infinitesimal semi-invariant pictures and co-amalgamation
• Horizontal and vertical mutation fans
• Exceptional sequences and rooted labeled forests