The Hilbert scheme $ X {[n] $ of a surface $ X $ describes collections of $ n $(not necessarily
distinct) points on $ X $. More precisely, it is the moduli space for $0 $-dimensional …

The purpose of this paper is to throw a bridge between two seemingly unrelated subjects.
One is the Hilbert scheme of points on projective surfaces, which has been intensively …

Although several authors have been interested in the Hilbert scheme Hilba (IP z)
parametrizing finite subschemes of length d in the projective plane ([I1, I2, F 1, F2, Br] among …

We give an algorithmic description of the action of the Chern classes of tautological bundles
on the cohomology of Hilbert schemes of points on a smooth surface within the framework of …

We give a motivated introduction to the theory of perverse sheaves, culminating in the
decomposition theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is …

We introduce the multigraded Hilbert scheme, which parametrizes all homogeneous ideals
with fixed Hilbert function in a polynomial ring that is graded by any abelian group. Our …

Gieseker-Nakajima moduli spaces $ M_ {k}(n) $ parametrize the charge $ k $
noncommutative $ U (n) $ instantons on ${\bf R}^{4} $ and framed rank $ n $ torsion free …

J. Emsalem and the author showed in [18] that a general polynomial $ f $ of degree $ j $ in
the ring $\mathcal {R}= k [{{y_1},\ldots,{y_r}}] $ has $\left ({\begin {array}{*{20}{c}}{j+ r-1}\\{r …

The body of mathematics developed in the last forty years or so which can be put under the
heading Singularity Theory is quite large. And the excellent introductions to this vast subject …

L'objet principal de ce travail est le théorème de division également baptisé «technique des
escaliers». Cette technique permet d'associer à chaque idéal de séries entières …