Hausdorff approximations and volume of tubes of singular algebraic sets

斜率零张量、Hodge结构的单值化形变以及管域的商

Slope zero tensors, uniformizing variations of Hodge structure and quotients of tube domains

该研究建立了刻画带klt奇点与丰沛典范除子的复射影簇的两种方法的等价性，构造了斜率零张量与单值化Hodge结构形变的互逆对应，推广了经典单值化结果，并证明了奇异Kähler–Einstein度量和乐群的紧性。

Explicit Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds

We exhibit the first non-trivial concrete examples of Gromov-Hausdorff compactifications of moduli spaces of Kähler-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.

Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below

We show that non-collapsed Gromov-Hausdorff limits of polarized Kahler manifolds, with Ricci curvature bounded below, are normal projective varieties, and the metric singularities of the limit space are precisely given by a countable union of analytic subvarieties. This extends a fundamental result of Donaldson-Sun, in which 2-sided Ricci curvature bounds were assumed. As a basic ingredient we show that, under lower Ricci curvature bounds, almost Euclidean balls in Kahler manifolds admit good holomorphic coordinates. Further applications are integral bounds for the scalar curvature on balls, a…

Collapsing hyperkähler manifolds

Given a projective hyperkahler manifold with a holomorphic Lagrangian fibration, we prove that hyperkahler metrics with volume of the torus fibers shrinking to zero collapse in the Gromov-Hausdorff sense (and smoothly away from the singular fibers) to a compact metric space which is a half-dimensional special Kahler manifold outside a singular set of real Hausdorff codimension 2 and is homeomorphic to the base projective space.

关于具有局部纤维化的奇异映射

On singular maps with local fibration

本文探讨了奇异局部管道纤维化存在的最一般条件，并给出了映射芽复合的一个应用。