Enriques曲面的度量退化与Satake紧化
Metric Degenerations and Satake Compactification of Enriques Surfaces
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中文总结 AI 辅助
本研究确定Enriques曲面上单位直径Ricci平坦Kähler度量模空间的Gromov–Hausdorff紧化，证明其度量退化由伴随Satake紧化编码，分类了所有相关GH极限。
中文摘要 AI 辅助
我们确定了Enriques曲面上单位直径Ricci平坦Kähler度量模空间的Gromov–Hausdorff紧化。我们证明所有度量退化都由Enriques周期域的伴随Satake紧化编码，该Satake紧化新增了32个边界分量，且每个边界处的GH极限均已确定。作为推论，Enriques曲面上Kähler Ricci平坦度量的所有GH极限都得到分类，包括固定复结构或固定极化的情况。
英文摘要
We determine the Gromov--Hausdorff compactification of the moduli space of unit-diameter Ricci-flat Kähler metrics on Enriques surfaces. We show that all metric degenerations are encoded by the adjoint Satake compactification of the Enriques period domain. There are 32 boundary components added in this Satake compactification, and the GH limit at each boundary is determined. As a corollary, all the GH limits of Kähler Ricci-flat metrics on Enriques surfaces are classified, including those for a fixed complex structure or a fixed polarization.
