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March 2022 The ring of modular forms for the even unimodular lattice of signature (2,18)
Atsuhira Nagano, Kazushi Ueda
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Hiroshima Math. J. 52(1): 43-51 (March 2022). DOI: 10.32917/h2021012

Abstract

We show that the ring of modular forms with characters for the even unimodular lattice of signature (2,18) is obtained from the invariant ring of $\mathrm {Sym}(\mathrm {Sym}^8(V)\oplus \mathrm {Sym}^{12}(V))$ with respect to the action of $\mathrm{SL}(V)$ by adding a Borcherds product of weight 132 with one relation of weight 264, where $V$ is a 2-dimensional $\mathbb C$-vector space. The proof is based on the study of the moduli space of elliptic K3 surfaces with a section.

Funding Statement

A. N. was partially supported by JSPS Kakenhi (18K13383) and MEXT LEADER. K. U. was partially supported by JSPS Kakenhi (16H03930).

Citation

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Atsuhira Nagano. Kazushi Ueda. "The ring of modular forms for the even unimodular lattice of signature (2,18)." Hiroshima Math. J. 52 (1) 43 - 51, March 2022. https://doi.org/10.32917/h2021012

Information

Received: 1 March 2021; Revised: 8 September 2021; Published: March 2022
First available in Project Euclid: 25 March 2022

Digital Object Identifier: 10.32917/h2021012

Subjects:
Primary: 14J15
Secondary: 11F55

Keywords: K3 surfaces , modular forms

Rights: Copyright © 2022 Hiroshima University, Mathematics Program

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Vol.52 • No. 1 • March 2022
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