Generalizations of the odd degree theorem and applications
LetV ⊂ ℙℝ n be an algebraic variety, such that its complexificationV ℂ ⊂ ℙ n is irreducible of codimensionm ≥ 1. We use a sufficient condition on a linear spaceL ⊂ ℙℝ n of dimensionm + 2r to have a nonempty intersection withV, to show that any six dimensional subspace of 5 × 5 real symmetric matrices contains a nonzero matrix of rank at most 3.
KeywordsTangent Bundle Algebraic Variety Euler Characteristic Chern Class Hyperplane Section
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