Schubert varieties, toric varieties and ladder determinantal varieties
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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...
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4.1.5. The weighted projective space P(q0, . . . ,qn), gcd(q0, . . . ,qn) = 1, is built from a fan in N = Z/Z(q0, . . . ,qn). Let ui ∈ N be the image of ei ∈ Z . The dual lattice is M = {(a0, . . . ,an) ∈ Z n+1 | a0q0+ · · ·+anqn = 0}. Also assume that gcd(q0, . . . , q̂i, . . . ,qn) = 1 for i = 0, . . . ,n. (a) Prove that the ui are the primitive ray generators of the fan giving P(q0, . . . ,qn...
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This note constructs the flat toric degeneration of the manifold Fln of flags in Cn from [GL96] as an explicit GIT quotient of the Gröbner degeneration in [KM03]. This implies that Schubert varieties degenerate to reduced unions of toric varieties, associated to faces indexed by rc-graphs (reduced pipe dreams) in the Gelfand–Cetlin polytope. Our explicit description of the toric degeneration of...
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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 ...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1997
ISSN: 0373-0956
DOI: 10.5802/aif.1590