The BCOV invariant of Camere-Garbagnati-Mongardi Calabi-Yau fourfolds is proportional to the author's equivariant torsion invariant and is expressed by Borcherds products in the Enriques and rational-curve-fixed-locus cases.
Analytic torsion for irreducible holomorphic symplectic fourfolds with involution, II: the singularity of the invariant (with an Appendix by Ken-Ichi Yoshikawa)
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abstract
We study the boundary behavior of the invariant of $K3^{[2]}$-type manifolds with antisymplectic involution, which we obtained using equivariant analytic torsion. We show the algebraicity of the singularity of the invariant by using the asymptotic of equivariant Quillen metrics and equivariant $L^2$-metrics. We prove that, in some cases, the invariant coincides with Yoshikawa's invariant for 2-elementary K3 surfaces. Hence, in these cases, our invariant is expressed as the Petersson norm of a Borcherds product and a Siegel modular form.
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Analytic torsion for irreducible holomorphic symplectic fourfolds with involution, III: relation with the BCOV invariant
The BCOV invariant of Camere-Garbagnati-Mongardi Calabi-Yau fourfolds is proportional to the author's equivariant torsion invariant and is expressed by Borcherds products in the Enriques and rational-curve-fixed-locus cases.