The irreducibility of ladder determinantal varieties
نویسندگان
چکیده
منابع مشابه
Hilbert functions of ladder determinantal varieties
We consider algebraic varieties de)ned by the vanishing of all minors of a )xed size of a rectangular matrix with indeterminate entries such that the indeterminates in these minors are restricted to lie in a ladder shaped region of the rectangular array. Explicit formulae for the Hilbert function of such varieties are obtained in (i) the rectangular case by Abhyankar (Rend. Sem. Mat. Univers. P...
متن کاملMixed Ladder Determinantal Varieties from Two-sided Ladders
We study the family of ideals defined by mixed size minors of two-sided ladders of indeterminates. We compute their Gröbner bases with respect to a skewdiagonal monomial order, then we use them to compute the height of the ideals. We show that these ideals correspond to a family of irreducible projective varieties, that we call mixed ladder determinantal varieties. We show that these varieties ...
متن کاملResultants of determinantal varieties
In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct generalization of the resultant of a very ample vector bundle [GKZ94], it corresponds to a necessary and sufficient condition so that a given morphism between two vector bundles on a projective variety ...
متن کاملOn Some Quiver Determinantal Varieties
We introduce certain quiver analogue of the determinantal variety. We study the Kempf-Lascoux-Weyman’s complex associated to a line bundle on the variety. In the case of generalized Kronecker quivers, we give a sufficient condition on when the complex resolves a maximal Cohen-Macaulay module supported on the quiver determinantal variety. This allows us to find the set-theoretical defining equat...
متن کاملA determinantal formula for the Hilbert series of one-sided ladder determinantal rings
We give a formula that expresses the Hilbert series of one-sided ladder determinantal rings, up to a trivial factor, in form of a determinant. This allows the convenient computation of these Hilbert series. The formula follows from a determinantal formula for a generating function for families of nonintersecting lattice paths that stay inside a one-sided ladder-shaped region, in which the paths...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1986
ISSN: 0021-8693
DOI: 10.1016/0021-8693(86)90134-1