Nonabelian Hodge theory for klt spaces and descent theorems for vector bundles
2019 ◽
Vol 155
(2)
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pp. 289-323
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Keyword(s):
To Come
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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.
1999 ◽
Vol 42
(2)
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pp. 209-213
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Keyword(s):
Keyword(s):
2004 ◽
Vol 134
(1)
◽
pp. 33-38
2001 ◽
Vol 130
(1)
◽
pp. 61-75
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1973 ◽
Vol 52
◽
pp. 173-195
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