De : Aldo Conca
Date : Jeu 31 Mai 2001 16:48
À : Marcel Morales
Objet : title and abstract
Name:
Aldo Conca
title:
Algebras of minors
abstracts:
In my talk I will present joint work with Winfried Bruns.
Let $I_t$ be the ideal generated by the minors of size $t$ of the
generic matrix
$X=(x_{ij}$ of size $m\times n$. Let $R(I)$ be the Rees algebra of
$I_t$, and let $A_t$ be the special fiber of $R(I)$, that is, the
subalgebra of $K[x_{ij}]$
generated by the $t$-minors of $X$. The algebras $A_t$ and $R(I)$ are
known to be normal
Cohen-Macaulay domains (if the characteristic is $0$ or large
enough). I will explain how
one can compute the divisor class group and the canonical class of
these algebras by using
the standard monomial theory and Gr\"obner-Sagbi deformations . As a
corollary, one has
that $A_t$ is Gorenstein iff\par
1) $t=min(m,n)$ (the Grassmannian) or \par
2) $t=1$ or $m=n$ and $t=m-1$ ($A_t$ is a polynomial ring in these cases)
or \par
3) $mn=t(m+n).$