Donaldson-Thomas theory and cluster algebras

Details Donaldson-Thomas theory and cluster algebras Donaldson-Thomas theory and cluster algebras

2010-02-26

arxiv.org/abs/1002.4884v2

Mathematics

Algebraic Geometry

39 pages, 8 figures, mostly rewritten

Scientific paper

We provide a transformation formula of non-commutative Donaldson-Thomas
invariants under a composition of mutations. Consequently, we get a description
of a composition of cluster transformations in terms of quiver Grassmannians.
As an application, we give an alternative proof of Fomin-Zelevinsky's
conjectures on $F$-polynomials and $g$-vectors.

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