Real Quartic Surfaces in RP_3 containing 16 Skew Lines

Abstract

In [BN] the authors construct a special complex of degree 20 over M, which for an open three dimensional set parametrizes smooth complex surfaces of degree four invariant which are Heisenberg invariant and each member of the family contains 32 lines but only 16 skew lines. The coordinates of the lines however need not be real. For a point l in a Zariski open set of M an algorithm is presented which evaluates the real coefficients of l in terms of the K-coordinates of l. The author uses a code in Maple which allows him to construct very explicite examples of real smooth Heisenberg invariant Kummer surfaces containing the special configuration of 16 real skew lines. An example is constructed at the end of the paper.