Abstract
Let
S
d
be the vector space of monomials of degree
d
in the variables
x
1
,...,
x
s
. For a subspace $V \sus S_d$ which is in general coordinates, consider the subspace $\gin V \sus S_d$ generated by initial monomials of polynomials in
V
for the revlex order. We address the question of what properties of
V
may be deduced from $\gin V$. % This is an approach for understanding what algebraic or geometric properties of a homogeneous ideal $I \sus k[x_1, ..., x_s]$ that may be deduced from its generic initial ideal $\gin I$.