Real K3 Surfaces without Real Points, Equivariant Determinant of the Laplacian, and the Borcherds Φ-function
نویسنده
چکیده
We consider an equivariant analogue of a conjecture of Borcherds. Let (Y, σ) be a real K3 surface without real points. We shall prove that the equivariant determinant of the Laplacian of (Y, σ) with respect to a σ-invariant Ricci-flat Kähler metric is expressed as the norm of the Borcherds Φ-function at the “period point”. Here the period of (Y, σ) is not the one in algebraic geometry.
منابع مشابه
Real K 3 Surfaces without Real Points ,
We consider an equivariant analogue of a conjecture of Borcherds. Let (Y,σ) be a real K3 surface without real points. We shall prove that the equivariant determinant of the Laplacian of (Y,σ) with respect to a σ-invariant Ricci-flat Kähler metric is expressed as the norm of the Borcherds Φ-function at the “period point”. Here the period of (Y,σ) is not the one in algebraic geometry.
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