Title: Vinberg-Conway chain terminates just after a supersingular symplectic 6-fold with 100 (-2) divisors

Abstract: Leech roots calculate fundamental domains of the hyperbolic lattices U+D_n up to n=22. Generalizing a result of Vinberg (1983, n=18), we apply this calculation for n < 21 to (semi-)automorphism groups of various K3 surfaces, and realize the case n=21 as the Picard lattice of the symplectic manifold in characteristic 2 in the title, which is expected to have an action of the Higman-Sims simple group.