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 …

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 …

In Chapter 1 we show that when a set D—(Q, P) of generator and relation degrees is given,
Q={q1:..., qu} and P={px,..., pw}, the family GorD of Gorenstein algebras A= R/J with J having …

We review the open problems in the theory of deformations of zero-dimensional objects,
such as algebras, modules or tensors. We list both the well-known ones and some new ones …

arXiv:math/0010107v2 [math.AG] 22 Feb 2001 Page 1 arXiv:math/0010107v2 [math.AG] 22
Feb 2001 Equations of Parametric Curves and Surfaces via Syzygies David A. Cox …

A polynomial is a direct sum if it can be written as a sum of two nonzero polynomials in some
distinct sets of variables, up to a linear change of variables. We analyze criteria for a …

We classify the orbits of nets of conics under the action of the projective linear group and we
determine the specializations of these orbits, using geometric and algebraic methods. We …

We prove that a standard realization of the direct image complex via the so-called Douady–
Barlet (Hilbert-Chow in the algebraic case) morphism associated with a smooth complex …

Ž. k X, X,..., X of codimension r. If ssr, we let PGor H be the space 1 2 s parametrizing all
graded Gorenstein R-algebras RrI with Hilbert function Ž Ž. Ž.. HH is dim RrI, with a scheme …

A continuous map Rm→ RN or Cm→ CN is called k-regular if the images of any k points are
linearly independent. Given integers m and ka problem going back to Chebyshev and …