Degeneration of Kähler-Einstein Manifolds II: The Toroidal Case

Orbifold K{ä}hler Groups related to arithmetic complex hyperbolic lattices

We study fundamental groups of toroidal compactifications of non compact ball quotients and show that the Shafarevich conjecture on holomorphic convexity for these complex projective manifolds is satisfied in dimension 2 provided the corresponding lattice is arithmetic and small enough. The method is to show that the Albanese mapping on an {é}tale covering space generates jets on the interior, if the lattice is small enough. We also explore some specific examples of Picard-Eisenstein type.

Collapsing of negative Kähler-Einstein metrics

In this paper, we study the collapsing behaviour of negative Kähler-Einstein metrics along degenerations of canonical polarized manifolds. We prove that for a toroidal degeneration of canonical polarized manifolds with the total space $\mathbb{Q}$-factorial, the Kähler-Einstein metrics on fibers collapse to a lower dimensional complete Riemannian manifold in the pointed Gromov-Hausdorff sense by suitably choosing the base points. Furthermore, the most collapsed limit is a real affine Kähler manifold.

环面或诺维科夫型基上的稳定性理论与典范修正

Stability theory over toroidal or Novikov type base and Canonical modifications

本文将代数几何中的稳定性理论推广到环面簇及其解析类似物，建立朗顿型Θ分层的（半）稳定约化定理，还探讨诺维科夫型环的应用，为K-稳定性与凯勒几何问题提供新框架。