The ring of modular forms for the even unimodular lattice of signature (2,18)

DOI10.32917/H2021012zbMATH Open1494.14033arXiv2102.09224OpenAlexW4220760578MaRDI QIDQ2134264

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Publication date: 6 May 2022

Published in: (Search for Journal in Brave)

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

m a t h r m S y m (m a t h r m {S y m}^{8} (V) o p l u s m a t h r m {S y m}^{12} (V))

with respect to the action of

m a t h r m S L (V)

by adding a Borcherds product of weight 132 with one relation of weight 264, where

V

is a 2-dimensional

m a t h b b C

-vector space. The proof is based on the study of the moduli space of elliptic K3 surfaces with a section.

Full work available at URL: https://arxiv.org/abs/2102.09224

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