3 citations · 8 across the 10 of their papers we have counts for
13 papers · 1 filter
On the separation Łojasiewicz exponents of real analytic sets in the real plane
Phi Dung Hoang, Hong Duc Nguyen
The main aim of the paper is to give a formula for computing the separation Łojasiewicz exponents for two real analytic set germs via the Newton--Puiseux expansions of their defini…
Motivic integration on special rigid varieties and the motivic integral identity conjecture
Hong Duc Nguyen
We prove in this paper the original version of Kontsevich and Soibelman's motivic integral identity conjecture for formal functions by developing a novel framework for equivariant…
Equivariant motivic integration on special formal schemes
Quy Thuong Lê, Hong Duc Nguyen
In this article, we construct an equivariant version of motivic integration on special formal schemes that generalizes our previous work for algebraic varieties. Pointing out the e…
Cohomology of contact loci
Nero Budur, Javier Fernández de Bobadilla, Quy Thuong Lê +1
We construct a spectral sequence converging to the cohomology with compact support of the m-th contact locus of a complex polynomial. The first page is explicitly described in term…
Parametrization simple irreducible plane curve singularities in arbitrary characteristic
Hong-Duc Nguyen
We study the classification of plane curve singularities in arbitrary characteristic. We first give a bound for the determinacy of a plane curve singularity with respect to pararam…
Equivariant motivic integration and proof of the integral identity conjecture for regular functions
Quy Thuong Lê, Hong Duc Nguyen
We develop the Denef-Loeser motivic integration to the equivariant motivic integration and use it to prove the full integral identity conjecture for regular functions.
Topological invariants of plane curve singularities: Polar quotients and Łojasiewicz gradient exponents
Hong-Duc Nguyen, Tien-Son Pham, Phi-Dung Hoang
In this paper, we study polar quotients and Łojasiewicz exponents of plane curve singularities, which are {\em not necessarily reduced}. We first show that the polar quotients is a…
Euler reflexion formulas for motivic multiple zeta functions
Quy Thuong Le, Hong Duc Nguyen
We introduce a new notion of $\boxast$-product of two integrable series with coefficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability and co…
Right unimodal and bimodal singularities in positive characteristic
Hong Duc Nguyen
The problem of classification of real and complex singularities was initiated by Arnol'd in the sixties who classified simple, unimodal and bimodal w.r.t. right equivalence. The cl…
Invariants of plane curve singularities and Plücker formulas in positive characteristic
Hong Duc Nguyen
We study classical invariants for plane curve singularities , an algebraically closed field of characteristic : Milnor number, delta invariant, kappa in…
The right classification of univariate power series in positive characteristic
Hong Duc Nguyen
While the classification of univariate power series up to coordinate change is trivial in characteristic 0, this classification is very different in positive characteristic. In thi…
Right simple singularities in positive characteristic
Gert-Martin Greuel, Nguyen Hong Duc
We classify isolated hypersurface singularities , an algebraically closed field of characteristic , which are simple w.r.t. right equivalence, that…
Some remarks on the planar Kouchnirenko's Theorem
Gert-Martin Greuel, Nguyen Hong Duc
We consider different notions of non-degeneracy, as introduced by Kouchnirenko (NND), Wall (INND) and Beelen-Pellikaan (WNND) for plane curve singularities and int…