We extend to higher dimension our valuative analysis of singularities of psh functions started in [FJ2]. Following [KoSo], we describe the geometry of the space V of all normalized valuations on C[z1, . . . , zn] centered at the origin. It is a union of simplices naturally endowed with an affine structure. Using relative positivity properties of divisors living on modifications of C n over the ...

The local Minkowski tensors are valuations on the space of convex bodies in Euclidean space with values in a space of tensor measures. They generalize at the same time the intrinsic volumes, the curvature measures and the isometry covariant Minkowski tensors that were introduced by McMullen and characterized by Alesker. In analogy to the characterization theorems of Hadwiger and Alesker, we giv...