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

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

2008-06-25

arxiv.org/abs/0806.4077v3

Mathematics

Algebraic Geometry

Terminology and a few typos corrected; Remark 4.5.5 updated

Scientific paper

Our main results concern complete intersections of three real quadrics. We prove that the maximal number $B^0_2(N)$ of connected components that a regular complete intersection of three real quadrics in $\Bbb{P}^N$ 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{$\frac14 N^2+O(N)$} and an upper bound \smash{$\frac38 N^2+O(N)$} for $B^0_2(N)$.

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