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Si stabilisce che le radici del polinomio totale di Chern dei fibrati vettoriali complessi sullo spazio proiettivo quaternionale di dimensione infinita sono quadrati di interi. Si trattano inoltre i casi di fibrati reali e quaternionali.
Let be a field and be the Grassmannian of -dimensional linear subspaces of . A map is called nesting if for every . Glover, Homer and Stong showed that there are no continuous nesting maps except for a few obvious ones. We prove a similar result for algebraic nesting maps , where is an algebraically closed field of arbitrary characteristic. For this yields a description of the algebraic sub-bundles of the tangent bundle to the projective space .
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