Nonabelian Hodge theory for klt spaces and descent theorems for vector bundles
Nonabelian Hodge theory for klt spaces and descent theorems for vector bundles
复制标题
klt 空间的非阿贝尔霍奇理论和向量丛的下降定理
作者：
D. Greb;Stefan Kebekus;T. Peternell;Behrouz Taji
我们将辛普森的非阿贝尔霍奇对应推广到具有川俣对数终端（klt）奇点的射影簇的背景。该证明依赖于沿着双有理态射的数值平坦向量丛的下降定理。以最简单的形式，该定理断言，给定任何 klt 变体 $X$ 和奇点的任何分辨率，分辨率上的任何向量丛在数字上似乎来自 $X$，确实来自 $X$ 。此外，出于独立的兴趣，建立了一个新的半稳定希格斯滑轮限制定理，该定理定义在正常射影簇的光滑轨迹上。
We generalise Simpson’s nonabelian Hodge correspondence to the context of projective varieties with Kawamata log terminal (klt) singularities. The proof relies on a descent theorem for numerically flat vector bundles along birational morphisms. In its simplest form, this theorem asserts that given any klt variety $X$ and any resolution of singularities, any vector bundle on the resolution that appears to come from $X$ numerically, does indeed come from $X$ . Furthermore, and of independent interest, a new restriction theorem for semistable Higgs sheaves defined on the smooth locus of a normal, projective variety is established.