The birational geometry of $$\overline{{\mathcal {R}}}_{g,2}$$ and Prym-canonical divisorial strata

Selecta Mathematica Pub Date : 2024-02-28 DOI:10.1007/s00029-023-00907-1

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Abstract

We prove that the moduli space of double covers ramified at two points ${\mathcal {R}}_{g,2}$ is uniruled for $3\le g\le 6$ and of general type for $g\ge 16$ . Furthermore, we consider Prym-canonical divisorial strata in the moduli space $\overline{{\mathcal {C}}^n{\mathcal {R}}}_g$ parametrizing n-pointed Prym curves, and we compute their classes in $\textrm{Pic}_{\mathbb {Q}}(\overline{{\mathcal {C}}^n{\mathcal {R}}}_g)$ .

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$$overline{/mathcal {R}}_{g,2}$ 和 Prym-canonical divisorial strata 的二元几何图形

Abstract 我们证明了在${\mathcal {R}}_{g,2}$ 两点处斜切的双盖的模空间对于$3\le g\le 6$ 是无iruled的，对于$g\ge 16$是一般类型的。此外，我们考虑了模空间 $\overline{{\mathcal {C}}^n{\mathcal {R}}}_g$ 中参数化 n 点 Prym 曲线的 Prym-canonical divisorial strata，并计算了它们在 $\textrm{Pic}_{\mathbb {Q}}(\overline{{\mathcal {C}}^n{\mathcal {R}}}_g)$ 中的类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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