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...
متن کاملDegeneracy Loci in CR Geometry
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 Section 5 of Chapter II is a summary of results appearing in my unpublished lecture no...
متن کاملNonemptiness 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...
متن کاملDegeneracy loci and polynomial equation solving
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)...
متن کاملPersistent orbital degeneracy in carbon nanotubes
The quantum-mechanical orbitals in carbon nanotube quantum dots are doubly degenerate over a large number of states. We argue that this experimental observation indicates that electrons are reflected without mode mixing at the nanotube-metal contacts. Two electrons occupying a pair of degenerate orbitals “shell” are found to form a triplet state starting from zero magnetic field. Finally, we ob...
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ژورنال
عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
سال: 2020
ISSN: 2036-2145,0391-173X
DOI: 10.2422/2036-2145.201804_016