On some varieties associated with trees

Frédéric Chapoton (1)

1 ICJ - Institut Camille Jordan

This article considers some affine algebraic varieties attached to finite trees and closely related to cluster algebras. Their definition involves a canonical coloring of vertices of trees into three colors. These varieties are proved to be smooth and to admit sometimes free actions of algebraic tori. Some results are obtained on their number of points over finite fields and on their cohomology.

Mots clés: tree; algebraic variety; independent set; cohomology

Domaines: Algèbres quantiques [math.QA]

Frédéric Chapoton. On some varieties associated with trees. The Michigan Mathematical Journal, 2015, 64 (4), pp.721-758. ⟨hal-00955085⟩