K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space IV: the structure of invariant

Shouhei Ma; Ken-Ichi Yoshikawa

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arXiv · 1506.00437

K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space IV: the structure of invariant

Shouhei Ma·Ken-Ichi Yoshikawa

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Abstract

A holomorphic torsion invariant of K3 surfaces with involution was introduced by the second-named author. In this paper, we completely determine its structure as an automorphic function on the moduli space of such K3 surfaces. On every component of the moduli space, it is expressed as the product of an explicit Borcherds lift and a classical Siegel modular form. We also introduce its twisted version. We prove its modularity and a certain uniqueness of the modular form corresponding to the twisted holomorphic torsion invariant. This is used to study an equivariant analogue of Borcherds' conjecture.

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Shouhei Ma, Ken-Ichi Yoshikawa. 2015-06-01. K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space IV: the structure of invariant. https://arxiv.org/abs/1506.00437

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