The total Betti number of the intersection of three real quadrics

TL;DR

This paper establishes a new upper bound for the total Betti number of the intersection of three quadrics in real projective space, improving upon classical bounds and providing insights into the topological complexity of such intersections.

Contribution

It introduces a tighter bound of n(n+1) for the total Betti number of intersections of three quadrics, surpassing previous classical bounds.

Findings

Bound of n(n+1) for Betti numbers of three quadrics intersection

Improved upon classical Barvinok's bound

Provides topological complexity insights for real algebraic intersections

Abstract

We prove that the total Betti number of the intersection X of three quadrics in RP^n is bounded by n(n+1). This bound improves the classical Barvinok's one which is at least of order three in n.