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Complexity of intersections of real quadrics and topology of symmetric determinantal varieties

Let X be the base locus of a linear system W of k quadrics. Let also S be the intersection of W with the discriminant hypersurface in the space of all homogeneous polynomials of degree two. We prove a formula relating the topology of X with the one of S and its (iterated) singular points. As a corollary we prove the sharp bound b(X)\leq O(n)^{k-1}.

preprint2012arXivOpen access
Antonio Lerario
math.AT
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Antonio Lerario

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