This book gives a comprehensive treatment of the singularities that appear in the minimal
model program and in the moduli problem for varieties. The study of these singularities and …

A study of the relation between a noetherian local domain with a given valuation and its
associated graded ring with respect to the valuation, which in some cases is an esentially …

This paper shows a finiteness property of a divisorial valuation in terms of arcs. First we
show that every divisorial valuation over an algebraic variety corresponds to an irreducible …

The notion of infinitely near singular points is classical and well under-stood for plane
curves. We generalize the notion to higher dimensions and to develop a general theory, in …

We consider the question of when a semigroup is the semigroup of a valuation dominating a
two-dimensional noetherian domain, giving some surprising examples. We give a necessary …

In this paper we study the Navier–Stokes boundary‐initial value problem in the exterior of a
rotating obstacle, in two and three spatial dimensions. We prove the local in time existence …

The notion of infinitely near singular points, classical in the case of plane curves, has been
generalized to higher dimensions in my earlier articles ([5],[6],[7]). There, some basic …

In [5], Cox introduced the homogeneous coordinate ring of a toric variety, which is a
polynomial ring that allows to show that such a variety behaves like a projective space in …

Suppose that R is an analytically irreducible or excellent local domain with maximal ideal m
R. We consider multiplicities and mixed multiplicities of R by filtrations of m R-primary ideals …

arxiv:2007.03459v1 [math.AG] 5 Jul 2020 Page 1 arxiv:2007.03459v1 [math.AG] 5 Jul 2020
EXAMPLES OF MULTIPLICITIES AND MIXED MULTIPLICITIES OF FILTRATIONS STEVEN …