Degeneracy Loci of Vector Bundle Maps and Ampleness
نویسندگان
چکیده
منابع مشابه
Schubert complexes and degeneracy loci
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...
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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 Section 5 of Chapter II is a summary of results appearing in my unpublished lecture no...
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Let V be a smooth equidimensional quasi-affine variety of dimension r over C and let F be a (p× s)-matrix of coordinate functions of C[V ], where s ≥ p+ r. The pair (V, F ) determines a vector bundle E of rank s− p over W := {x ∈ V | rkF (x) = p}. We associate with (V, F ) a descending chain of degeneracy loci of E (the generic polar varieties of V represent a typical example of this situation)...
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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...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 2002
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-14359