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- W1490286885 abstract "We characterize those unipotent representations of the fundamental group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=pi 1 left-parenthesis upper X comma x right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>π<!-- π --></mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>pi _1(X,x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of a compact Kähler manifold <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, which correspond to a Higgs bundle whose underlying Higgs field is equal to zero. The characterization is parallel to the one that R. Hain gave of those unipotent representations of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=pi 1 left-parenthesis upper X comma x right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>π<!-- π --></mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>pi _1(X,x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> that can be realized as the monodromy of a flat connection on the holomorphically trivial vector bundle. We see that Hain’s result and ours follow from a careful study of Simpson’s correspondence between Higgs bundles and local systems." @default.
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- W1490286885 date "2004-12-28" @default.
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- W1490286885 title "Unipotent flat bundles and Higgs bundles over compact Kähler manifolds" @default.
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- W1490286885 doi "https://doi.org/10.1090/s0002-9947-04-03652-9" @default.
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