Explicit Gromov-Hausdorff compactifications of moduli spaces of K\"ahler-Einstein Fano manifolds
Explicit Gromov-Hausdorff compactifications of moduli spaces of K\"ahler-Einstein Fano manifolds
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DOI：
10.4310/pamq.2017.v13.n3.a5
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发表时间：
2017-04
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影响因子：
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通讯作者：
Cristiano Spotti;Song Sun
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文献类型：
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作者：
Cristiano Spotti;Song Sun
我们给出了在大于2的所有复维中K ahler-Einstein Fano流形的模空间（Fano K-模空间）的Gromov-Hausdorff紧化的第一个非平凡的具体例子.我们还讨论了显式研究具有大反正则体积的K-稳定Fano流形的模空间的潜在应用。我们的论点是基于最近的进展有关几何的度量切锥和相关的想法的代数几何研究的奇异性的K-稳定的Fano品种。
We exhibit the first non-trivial concrete examples of Gromov-Hausdorff compactifications of moduli spaces of K\"ahler-Einstein Fano manifolds in all complex dimensions bigger than two (Fano K-moduli spaces). We also discuss potential applications to explicit study of moduli spaces of K-stable Fano manifolds with large anti-canonical volume. Our arguments are based on recent progress about the geometry of metric tangent cones and on related ideas about the algebro-geometric study of singularities of K-stable Fano varieties.