K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space II: a structure theorem for r(M)>10

摘要

We study the structure of the invariant of K3 surfaces with involution, whichwe obtained using equivariant analytic torsion. It was known before that theinvariant is expressed as the Petersson norm of an automorphic form on themoduli space. When the rank of the invariant sublattice of the K3-lattice withrespect to the involution is strictly bigger than 10, we prove that thisautomorphic form is expressed as the tensor product of an explicit Borcherdslift and Igusa's Siegel modular form.