Rational points on singular intersections of quadrics

Abstract

Abstract Given an intersection of two quadrics $X\subset { \mathbb{P} }^{m- 1} $ , with $m\geq 9$ , the quantitative arithmetic of the set $X( \mathbb{Q} )$ is investigated under the assumption that the singular locus of $X$ consists of a pair of conjugate singular points defined over $ \mathbb{Q} (i)$ .