A New Look at the Kummer Surface

Abstract

Kummer's surface has the base surface F of a certain net of quadrics in [5] for a non-singular model. All the quadrics of have a common self-polar simplex ∑, and can, in a double-infinity of ways, be based on a quadric Ω1 and two quadrics that Ω1 reciprocates into each other. F is invariant under harmonic inversions in the vertices and opposite bounding primes of ∑ and (§2) contains 32 lines. In §3 it is shown, conversely, that those quadrics for which a given simplex is self-polar and which contain a line of general position constitute a net of this kind.