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
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
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