01015nas a2200109 4500008004100000245004300041210004300084260001300127520070800140100002100848856003600869 2012 en d00aConvex pencils of real quadratic forms0 aConvex pencils of real quadratic forms bSpringer3 aWe study the topology of the set X of the solutions of a system of two
quadratic inequalities in the real projective space RP^n (e.g. X is the
intersection of two real quadrics). We give explicit formulae for its Betti
numbers and for those of its double cover in the sphere S^n; we also give
similar formulae for level sets of homogeneous quadratic maps to the plane. We
discuss some applications of these results, especially in classical convexity
theory. We prove the sharp bound b(X)\leq 2n for the total Betti number of X;
we show that for odd n this bound is attained only by a singular X. In the
nondegenerate case we also prove the bound on each specific Betti number
b_k(X)\leq 2(k+2).1 aLerario, Antonio uhttp://hdl.handle.net/1963/7099