On the number of components of a complete intersection of real quadrics

Abstract

Our main results concern complete intersections of three real quadrics. We prove that the maximal number $B_2^0(N)$ of connected components that a regular complete intersection of three real quadrics in ${\mathbb{P}}^N$ can 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 \smash{$\frac{1}{4}{N}^2+O(N)$} and an upper bound \smash{$\frac{3}{8}{N}^2+O(N)$} for $B_2^0(N)$.

Terminology and a few typos corrected; Remark 4.5.5 updated

Cited by in corpus (3)

• Complexity of intersections of real quadrics and topology of symmetric determinantal varieties
• Convex pencils of real quadratic forms
• Intrinsic volumes of set of singular matrices