Denominator vectors and dimension vectors from triangulated surfaces

In a categorification of skew-symmetric cluster algebras,each cluster variable corresponds with an indecomposablemodule over the associated Jacobian algebra. Buan, Marshand Reiten studied when the denominator vector of eachcluster variable in an acyclic cluster algebra coincides with thedimension vector of the corresponding module. In this paper,we give analogues of their results for cluster algebras fromtriangulated surfaces by comparing two kinds of intersectionnumbers of tagged arcs.