The connectedness of degeneracy loci
نویسندگان
چکیده
منابع مشابه
Nonemptiness of Symmetric Degeneracy Loci
Let V be a renk N vector bundle on a d-dimensional complex projective scheme X; assume that V is equipped with a quadratic form with values in a line bundle L and that SV ∗ ⊗ L is ample. Suppose that the maximum rank of the quadratic form at any point of X is r > 0. The main result of this paper is that if d > N − r, the locus of points where the rank of the quadratic form is at most r − 1 is n...
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Starting on the next page is the 16-page Chapter II excerpted from my dissertation, “Enumeration and Normal Forms for Singularities in CauchyRiemann Structures,” 1997, University of Chicago. I have made a few minor editorial modifications so that Chapter II can be read without referring to the other Chapters. Section 5 of Chapter II is a summary of results appearing in my unpublished lecture no...
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The classical Thom–Porteous formula expresses the homology class of the degeneracy locus of a generic map between two vector bundles as an alternating sum of Schur polynomials. A proof of this formula was given by Pragacz by expressing this alternating sum as the Euler characteristic of a Schur complex, which gives an explanation for the signs. Fulton later generalized this formula to the situa...
متن کاملNonemptiness of Skew-symmetric Degeneracy Loci
Let V be a rank N vector bundle on a d-dimensional complex projective scheme X; assume that V is equipped with a skewsymmetric bilinear form with values in a line bundle L and that ΛV ∗⊗L is ample. Suppose that the maximum rank of the form at any point of X is r, where r > 0 is even. The main result of this paper is that if d > 2(N − r), then the locus of points where the rank of the form is at...
متن کاملDegeneracy Loci Formulas for Morphisms with Symmetries
0. The goal of the present note is to give new explicit formulas for the fundamental classes of degeneracy loci associated with the following vector bundles homomorphisms. For a given pair B A of vector bundles, we denote by B _ A (resp. B ^ A) the image of the canonical composition B A ! A A S 2 A (resp. B A ! A A 2 (A)).
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 1990
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-26-2-235-248