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Nonabelian Hodge theory for klt spaces and descent theorems for vector bundles
- Part of
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- Journal:
- Compositio Mathematica / Volume 155 / Issue 2 / February 2019
- Published online by Cambridge University Press:
- 07 February 2019, pp. 289-323
- Print publication:
- February 2019
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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.
