K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space
By K. Yoshikawa. 2004
60 citations recorded by the source corpus.
In this paper, we introduce an invariant of a K3 surface with ℤ2-action equipped with a ℤ2-invariant Kähler metric, which we obtain using the equivariant analytic torsion of the trivial line bundle. This invariant is shown to be independent of the choice of the Kähler metric. It can be viewed as a function on the moduli space of K3 surfaces with involution. The main result of this paper is that this function can be identified with an automorphic form, which characterizes the discriminant locus. In particular, we show that the Ray–Singer analytic torsion of the trivial line bundle on an Enriques surface with Ricci-flat Kähler metric is given by the value of the norm of the Borcherds Φ-function at its period point.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d7e95aa7706bcd0469a1c20d1264640bb242443e
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In Applied Mathematics
- Zhiqin Lu
- H. Fang
- G'abor Sz'ekelyhidi
- Duong H. Phong
- Jacob Sturm
- Xiaowei Wang
- Kento Fujita
- L. Charles
In Geometry and Topology
- Zhiqin Lu
- H. Fang
- K. Yoshikawa
- G'abor Sz'ekelyhidi
- Duong H. Phong
- Jacob Sturm
- Xiaowei Wang
- Kento Fujita
Citations in the corpus
- ANALYTIC TORSION FOR CALABI-YAU THREEFOLDS (2006, methodology): “…by the Grants-in-Aid for Scientific Research for Encouragement of Young Scientists (B) 16740030, JSPS. 1 By making use of the curvature formula for Quillen metrics [11], BershadskyCecotti-Ooguri-Vafa obtained a variational formula for the BCOV torsion of Ricciflat Calabi-Yau manifolds [7].”