Corpus ID: 237605290

Modularity and uniformization of a higher genus algebraic space curve, Hilbert's 22nd problem and $E_6$, $E_7$, $E_8$-singularities

@inproceedings{Yang2021ModularityAU,
  title={Modularity and uniformization of a higher genus algebraic space curve, Hilbert's 22nd problem and \$E\_6\$, \$E\_7\$, \$E\_8\$-singularities},
  author={Lei Yang},
  year={2021}
}
  • Lei Yang
  • Published 23 September 2021
  • Mathematics
We prove the modularity for an algebraic space curve $Y$ of genus $50$ in $\mathbb{P}^5$, which consists of $21$ quartic polynomials in six variables, by means of an explicit modular parameterizations by theta constants of order $13$. This provides an example of modularity for higher genus space curve as well as an explicit uniformization of algebraic space curves of higher genus and a hyperbolic uniformization of arithmetic type for a higher genus arithmetic algebraic curve. In particular, it… Expand