Topology of a system of two quadratic inequalities

Details Topology of a system of two quadratic inequalities Topology of a system of two quadratic inequalities

2011-06-23

arxiv.org/abs/1106.4678v2

Mathematics

Algebraic Geometry

Scientific paper

We study the topology of the set of the (spherical, projective and affine) solutions of a system of two quadratic inequalities: we give explicit formulas for its Betti numbers and give some sharp estimates for them; we also give a bound linear in n for the topological complexity of the intersection of two quadrics in RP^n. We study the geometry of generic pencils of quadrics. We discuss some applications of the previous results.

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