Cubic fourfolds with eleven cusps and a related moduli space

Abstract

First we construct a cubic 4-fold whose singularities are 11 cusps and which has an action of the Mathieu group 𝘔₁₁, all over the ternary field l𝔽₃ . We next consider a certain moduli space of bundles on a supersingular K3 surface of Artin invariant one in characteristic 3. We show that it has 275 (-2) Mukai vectors which form the McLaughlin graph, and ask questions on it and on its relation with our 𝘔₁₁-cubic 4-fold.