论文标题
带来的曲线：新旧
Bring's curve: Old and New
论文作者
论文摘要
Bring's Curve是带有自动形态组$ S_5 $的独特的Riemann Surface-4的曲线，具有许多非凡的属性。我们审查，提供新的证据并扩展了许多这些证明，包括为平面曲线模型的自动形态组的完整实现，确定了曲线的新椭圆形商$ x_0（50）$，提供了对theta特征的轨道分解的完整描述，并确定了s varient varisors s divisors s divise的特征。在实现这一目标时，我们在Sagemath，MacAulay2和Maple中使用了现代计算工具，为此，提供了调查计算的笔记本。
Bring's curve, the unique Riemann surface of genus-4 with automorphism group $S_5$, has many exceptional properties. We review, give new proofs of, and extend a number of these including giving the complete realisation of the automorphism group for a plane curve model, identifying a new elliptic quotient of the curve and the modular curve $X_0(50)$, providing a complete description of the orbit decomposition of the theta characteristics, and identifying the unique invariant characteristic with the divisor of the Szëgo kernel. In achieving this we have used modern computational tools in Sagemath, Macaulay2, and Maple, for which notebooks demonstrating calculations are provided.
