On the Number of Components of a Complete Intersection of Real Quadrics

Abstract

AbstractOur main results-5pc]Please check the text is ok? concern complete intersections of three real quadrics. We prove that the maximal number B20(N) of connected components that a regular complete intersection of three real quadrics in ℙNmay have differs at most by one from the maximal number of ovals of the submaximal depth \([(N - 1)/2]\)of a real plane projective curve of degree \(d = N + 1\). As a consequence, we obtain a lower bound \(\frac{1} {4}{N}^{2} + O(N)\)and an upper bound \(\frac{3} {8}{N}^{2} + O(N)\)for B20(N).KeywordsBetti numberQuadricComplete intersectionTheta characteristic