2001/01/13 by Winfried Bruns, Bruns, Winfried, Aldo Conca +1
Mathematics · #13A30 #13C20 #13F50 #14M12 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13A30 #msc:13C20 #msc:13F50 #msc:14M12
paper · pdf · doi:10.48550/arxiv.math/0101117
17 pages
arxiv created 2004/01/29 · arxiv updated 2009/11/30
Let X be an n× m matrix of indeterminates over a field K (of sufficiently large characteristic) and Mt the set of m-minors of X. We consider two objects: (1) the Ress algebra of the polynomial ring K[X] with respect to the ideal It generated by Mt, and (2) the At subalgebra of K[X] generated by Mt. Note that At is tHE coordinate ring of a Grassmannian if t=min(m,n); also the cases t=1 and t=m-1=n-1 are easily understood, since At is a polynomial ring over K in these cases. For both objects we compute the divisor class group and the canonical class. In particular we determine the Gorenstein rings among the At. It turns out that At is Gorenstein exactly in the cases listed above and when t(m+n)=mn. We use initial methods, based on the straightening law and KRS. They can be applied to other types of determinantal ideals, too. We do this explicitly for generic Hankel matrices.