Analytic torsion for irreducible holomorphic symplectic fourfolds with involution, I: Construction of an invariant

In this paper, we construct an invariant for irreducible holomorphic symplectic manifolds of $K{3}^{[2]}$-type with antisymplectic involution by using the equivariant analytic torsion. Moreover, we give a formula for the complex Hessian of the logarithm of the invariant.