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) $mn=t(m+n).$