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Explicit equations of the Cartwright-Steger surface

Lev A. Borisov, Sai-Kee Yeung

Abstract

We construct explicit equations of Cartwright-Steger and related surfaces.

Explicit equations of the Cartwright-Steger surface

Abstract

We construct explicit equations of Cartwright-Steger and related surfaces.

Paper Structure

This paper contains 6 sections, 4 theorems, 35 equations, 8 tables.

Table of Contents

  1. Introduction
  2. Constructing the surface $Z_3=\widehat{\mathcal{B}^2/\mathop{\mathrm{Ker}}\nolimits(\rho_3)}$
  3. On the quotient of CS surface by the cyclic group of order three.
  4. Constructing 21-fold cover of CS surface
  5. Constructing CS surface
  6. Verification

Key Result

Proposition \oldthetheorem

Up to a choice of square root of $(-1)$, the action of $G$ on $H^0(Z_3,K_{Z_3})$ is given by the direct sum of irreducible representations $\chi_2 +\chi_4$. The equations on $\mathop{\mathrm{Sym}}\nolimits^2(\chi_2 + \chi_4)$ are given as follows. We have $\mathop{\mathrm{Sym}}\nolimits^2(\chi_2) =

Theorems & Definitions (21)

  • Proposition \oldthetheorem
  • proof
  • Remark \oldthetheorem
  • Remark \oldthetheorem
  • Proposition \oldthetheorem
  • proof
  • Remark \oldthetheorem
  • Remark \oldthetheorem
  • Proposition \oldthetheorem
  • proof
  • ...and 11 more