Reye congruences

Abstract

This paper studies the congruences of lines which are included in two distinct quadrics of a given generic three-dimensional projective space of quadrics in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper P cubed"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">P</mml:mi> </mml:mrow> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{{\mathbf {P}}^3}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> .