The total Betti number of the intersection of three real quadrics
Antonio Lerario · Advances in Geometry · 2014
Abstract The classical Barvinok bound for the sum of the Betti numbers of the intersection X of three quadrics in ℝPn says that there exists a natural number a such that b(X) ≤ n3a. We improve this bound proving the inequality b(X) ≤ n(n+1). Moreover we show that this bound is asymptotically sharp as n goes to infinity.