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Now showing items 1-10 of 17

#### On the generalized Nash problem for smooth germs and adjacencies of curve singularities

(2017-12-10)

In this paper we explore the generalized Nash problem for arcs on a germ of smooth surface: given two prime divisors above its special point, to determine whether the arc space of one of them is included in the arc space ...

#### Homogeneous singularity and the Alexander polynomial of a projective plane curve

(2017-12-10)

The Alexander polynomial of a plane curve is an important invariant in global theories on curves. However, it seems that this invariant and even a much stronger one the fundamental group of the complement of a plane curve ...

#### Topology of Spaces of Valuations and Geometry of Singularities

(2017-11-11)

Given an algebraic variety X defined over an algebraically closed field, we study the space RZ(X,x) consisting of all the valuations of the function field of X which are centered in a closed point x of X. We concentrate ...

#### A proof of the integral identity conjecture, II

(2017-10-31)

In this note, using Cluckers-Loeser’s theory of motivic integration, we prove the integral identity conjecture with framework a localized Grothendieck ring of varieties over an arbitrary base field of characteristic zero.

#### Right unimodal and bimodal singularities in positive characteristic

(2017-08-07)

The problem of classification of real and complex singularities was initiated by Arnol'd in the sixties who classified simple, unimodal and bimodal singularities w.r.t. right equivalence. The classification of simple ...

#### Representation of surface homeomorphisms by tête-à-tête graphs

(2017-06-21)

We use tête-à-tête graphs as defined by N. A'campo and extended versions to codify all periodic mapping classes of an orientable surface with non-empty boundary, improving work of N. A'Campo and C. Graf. We also introduce ...

#### On intersection cohomology with torus actions of complexity one

(2017-05-20)

The purpose of this article is to investigate the intersection cohomology for algebraic varieties with torus action. Given
an algebraic torus T, one of our result determines the intersection cohomology Betti numbers of ...

#### Non-normal affine monoids, modules and Poincaré series of plumbed 3-manifolds

(2017-05-18)

We construct a non-normal affine monoid together with its modules associated with a negative definite plumbed 3-manifold M. In terms of their structure, we describe the $H_1(M,\mathbb{Z})$-equivariant parts of the topological ...

#### Euler reflexion formulas for motivic multiple zeta functions

(2017-05-14)

We introduce a new notion of $\boxast$-product of two integrable series with coefficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability of and commuting with the limit of rational ...

#### A Short Survey on the Integral Identity Conjecture and Theories of Motivic Integration

(2017-04-04)

In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these ...