تقرير
Compactifications of moduli space of (quasi-)trielliptic K3 surfaces
العنوان: | Compactifications of moduli space of (quasi-)trielliptic K3 surfaces |
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المؤلفون: | Chen, Yitao, Wu, Haoyu, Yao, Hanyu |
سنة النشر: | 2022 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Algebraic Geometry, 14J15, 14J28, 14J70, 14L24 |
الوصف: | We study the moduli space $\mathcal{F}_{T_1}$ of quasi-trielliptic K3 surfaces of type I, whose general member is a smooth bidegree $(2,3)$-hypersurface of $\mathbb{P}^1\times \mathbb{P}^2$. Such moduli space plays an important role in the study of the Hassett-Keel-Looijenga program of the moduli space of degree $8$ quasi-polarized K3 surfaces. In this paper, we consider several natural compactifications of $\mathcal{F}_{T_1}$, such as the GIT compactification and arithmetic compactifications. We give a complete analysis of GIT stability of $(2,3)$-hypersurfaces and provide a concrete description of the boundary of the GIT compactification. For the Baily--Borel compactification of the quasi-trielliptic K3 surfaces, we also compute the configurations of the boundary by classifying certain lattice embeddings. As an application, we show that $(\mathbb{P}^1\times \mathbb{P}^2,\epsilon S)$ with small $\epsilon$ is K-stable if $S$ is a K3 surface with at worst ADE singularities. This gives a concrete description of the boundary of the K-stability compactification via the identification of the GIT stability and the K-stability. We also discuss the connection between the GIT, Baily--Borel compactification, and Looijenga's compactifications by studying the projective models of quasi-trielliptic K3 surfaces. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2212.14635 |
رقم الأكسشن: | edsarx.2212.14635 |
قاعدة البيانات: | arXiv |
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