  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 $\gin
I$.

Algebraic Geometry;Commutative Algebra;Algebraic Geometry