论文标题
渐近锥形calabi-yau歧管的分类
Classification of asymptotically conical Calabi-Yau manifolds
论文作者
论文摘要
根据定义，riemannian锥$（c，g_c）$是扭曲的产品$ c = \ mathbb {r}^+ \ times l $，带公制$ g_c = dr^2 \ oplus r^2 g_l $，其中$（l，g_l）$是无边界的紧凑型riemann歧管。我们说，如果$ g_c $是ricci-flatkähler公制，并且如果$ c $允许$ g_c $ -parallel holomorthic卷表格；这相当于横截面$（l，g_l）$是Sasaki-Einstein歧管。在本文中，我们将所有平滑完整的Calabi-yau歧管渐近地分类与某些给定的calabi-yau锥体渐近，以无穷大的多项式速率。作为特殊情况，这包括克朗海默对无扭动理论的啤酒hyper-kähler的分类$ 4 $ - manifolds。
A Riemannian cone $(C, g_C)$ is by definition a warped product $C = \mathbb{R}^+ \times L$ with metric $g_C = dr^2 \oplus r^2 g_L$, where $(L,g_L)$ is a compact Riemannian manifold without boundary. We say that $C$ is a Calabi-Yau cone if $g_C$ is a Ricci-flat Kähler metric and if $C$ admits a $g_C$-parallel holomorphic volume form; this is equivalent to the cross-section $(L,g_L)$ being a Sasaki-Einstein manifold. In this paper, we give a complete classification of all smooth complete Calabi-Yau manifolds asymptotic to some given Calabi-Yau cone at a polynomial rate at infinity. As a special case, this includes a proof of Kronheimer's classification of ALE hyper-Kähler $4$-manifolds without twistor theory.
