Automorphisms of Supersingular K3 Surfaces and Salem Polynomials

We use the notation defined in this paper. Let X be a supersingular K3 surface in characteristic p = p with Artin invariant σ = sigma. • GramSX[p, sigma] is a Gram matrix of the lattice Λp,σ, which is isomorphic to SX . • h0[p, sigma] is a vector h0 of Λp,σ with ⟨h0, h0⟩Λ > 0. • Rh0[p, sigma] is the set R(h0). • amplelist[p, sigma] is an ample list of vectors a = [h0, ρ1, . . . , ρK ]. We identify D(a) with N(X) by a suitable isometry Λp,σ →∼ SX . • sizeMs[p, sigma] is the length l of the list [M(h1), . . . ,M(hl)] of matrix representations of double plane involutions τ(hi) ∈ Aut(X) whose product τ(h1) · · · τ(hl) is of irreducible Salem type.