In one sense, deformation theory is as old as algebraic geometry itself: this is because all
algebro-geometric objects can be “deformed” by suitably varying the coef? cients of their …

1. Introduction Page 1 T,Q-CATALAN NUMBERS AND THE HILBERT SCHEME MARK
HAIMAN 1. Introduction In 9], A. Garsia and the present author introduced a new bivariate `q-analog' …

A very beautiful line of algebraic inquiry, going back to Macaulay, deals with the following
question: for W HO (Opr (d)) a linear subspace of a given dimension, what is the smallest …

Equivariant compactifications of reductive groups can be described by combinatorial data.
On the other hand, equivariant compactifications of the additive group G^ n_a are more …

This paper outlines a new general construction, named “multi-space”, that forms the proper
geometrical foundation for the numerical analysis of differential equations–in direct analogy …

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 …

Let $ R={\Bbb C}[x_1, x_2,\ldots, x_n]/(f_1,\ldots, f_m) $ be a positively graded Artinian
algebra. A long-standing conjecture in algebraic geometry, differential geometry, and …

1. Introduction. Of the completely integrable Hamiltonian systems, those which are
algebraically integrable [AvM1],[AvM2],[vM] occupy a privileged position. Roughly speaking …

The moduli space of rank-n commutative algebras equipped with an ordered basis is an
affine scheme 3n of finite type over Z, with geometrically connected fibers. It is smooth if and …

The punctual Hilbert scheme has been known since the early days of algebraic geometry in
EGA style. Indeed it is a very particular case of the Grothendieck's Hilbert scheme which …