Corpus ID: 221534569

$E_8$-singularity, invariant theory and modular forms

@article{Yang2020E\_8singularityIT,
  title={\$E\_8\$-singularity, invariant theory and modular forms},
  author={Lei Yang},
  journal={arXiv: Number Theory},
  year={2020}
}
  • Lei Yang
  • Published 7 September 2020
  • Mathematics
  • arXiv: Number Theory
As an algebraic surface, the equation of $E_8$-singularity $x^5+y^3+z^2=0$ can be obtained from a quotient $C_Y/\text{SL}(2, 13)$ over the modular curve $X(13)$, where $Y \subset \mathbb{CP}^5$ is an algebraic curve given by a system of $\text{SL}(2, 13)$-invariant polynomials and $C_Y$ is a cone over $Y$. It is different from the Kleinian singularity $\mathbb{C}^2/\Gamma$, where $\Gamma$ is the binary icosahedral group. This gives a negative answer to Arnol'd and Brieskorn's questions about… Expand

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