Cohomology of real three-dimensional triquadrics

The total Betti number of the intersection of three real quadrics

“…Moreover, upon suggestion of the referee, using results from [12] we can show this bound is asymptotically sharp as n goes to infinity.…”

“…Similarly for even n the author of [12] is able to produce a complete intersection M of three real quadrics in CP n such that (1 + (−1) n ).…”

“…As pointed out to the author by the referee, a series of papers of Krasnov is dedicated to the cohomology of the intersection of three quadrics: in [11] the cohomology of a nonsingular three-dimensional intersection of three quadrics is computed using the spectral sequence of [3]; in [12] the existence of maximal complete intersections of three quadrics is proved. In particular Theorem 0.3 and Corollary 0.4 from [11] say that for every odd n there exists a complete intersection M of real quadrics in CP n such that…”

“…A. Agrachev: the main idea of this paper is a natural development of one of his intuitions. The author wishes to thank also the anonymous referee for her/his valuable suggestions and for pointing out to him the papers [11] and [12].…”