K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space III: the case r(M)\geq18

TL;DR

This paper establishes the automorphic nature of an invariant for K3 surfaces with involution, using equivariant analytic torsion, specifically in low-dimensional moduli spaces (dimension ≤ 2).

Contribution

It extends the understanding of automorphic properties of invariants associated with K3 surfaces with involution to cases with small moduli space dimensions.

Findings

Proves automorphic property of the invariant for r(M) ≥ 18.

Uses equivariant analytic torsion in the proof.

Focuses on moduli spaces of dimension ≤ 2.

Abstract

We prove the automorphic property of the invariant of K3 surfaces with involution, which we obtained using equivariant analytic torsion, in the case where the dimension of the moduli space is less than or equal to 2.