Abstract We study birational projective models of 𝓜2,2 obtained from the moduli space of curves with nonspecial divisors. We describe geometrically which singular curves appear in these models and show that one of them is obtained by blowing down the Weierstrass divisor in the moduli stack of 𝓩-stable curves 𝓜2,2(𝓩) defined by Smyth. As a corollary, we prove projectivity of the coarse moduli space M2,2(𝓩).

中文翻译：

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𝓜2,2 的双有理模型作为具有非特殊因数的曲线的模而产生

摘要 我们研究了从具有非特殊因数的曲线的模空间中获得的 𝓜2,2 的双有理射影模型。我们从几何上描述了这些模型中出现哪些奇异曲线，并表明其中之一是通过吹低 Smyth 定义的 𝓩-稳定曲线 𝓜2,2(𝓩) 模堆中的 Weierstrass 除数而获得的。作为推论，我们证明了粗模空间 M2,2(𝓩) 的射影性。