We generalize the Białynicki-Birula decomposition from actions of G m on smooth varieties
to actions of a linearly reductive group G on finite type schemes and algebraic spaces. We …

The Hilbert scheme of points of a smooth surface is a well-studied parameter space, lying at
the interface of algebraic geometry, commutative algebra, representation theory …

Sets of zero-dimensional ideals in the polynomial ring k [x, y] that share the same leading
term ideal with respect to a given term ordering are known to be affine spaces called …

In the local setting, Gr\" obner cells are affine spaces that parametrize ideals in $\mathbf
{k}[\![x, y]\!] $ that share the same leading term ideal with respect to a local term ordering. In …

We study the locus of the liftings of a homogeneous ideal H in a polynomial ring over any
field. We prove that this locus can be endowed with a structure of scheme LH by applying …

Abstract We let A= R/I be a standard graded Artinian algebra quotient of R= k [x, y], the
polynomial ring in two variables over a field k by an ideal I, and let n be its vector space …

We begin with a comprehensive discussion of the punctual Hilbert scheme of the regular two-
dimensional local ring in terms of the Gröbner cells. These schemes are the most …

This thesis presents an algorithm to find the local structure of intersections of plane curves.
More precisely, we address the question of describing the scheme of the quotient ring of a …

Die vorliegende Dissertation besteht aus zwei Kapiteln zu zwei unterschiedlichen
Anwendungen von Toruswirkungen in der algebraischen Geometrie. Die wichtigsten …

[spa] En esta tesis abordamos el problema de la aproximación de anillos locales por anillos
de Gorenstein en el caso cero-dimensional. Nos centramos en el estudio y el cálculo …