16 research outputs found
Decomposition, purity and fibrations by normal crossing divisors
We give a simple geometric proof of the decomposition theorem in terms of
Thom-Whitney stratifications by reduction to fibrations by normal crossings
divisors over the strata and explain the relation with the local purity theorem
an unpublished result of Deligne and Gabber.Comment: arXiv admin note: text overlap with arXiv:1302.581
Integrable Harmonic Higgs Bundles With Vanishing And Eigenvalues of
We study the tt*-geometry with vanishing endormorphism . Given
an integrable harmonic Higgs bundle on
a complex manifold , Firstly we prove that, under the \emph{IS} condition,
vanishing implies vanishing Higgs field and the Chern
connection of the Hermitian Einstein metric is a holomorphic connection, so
the metric and are invariant. Secondly, without the \emph{IS}
condition, we show that vanishing will imply vanishing Higgs
field if we assume that the Chern connection of is a holomorphic
connection. Finally, we add real structure . Given any
\emph{CV}-structure, we prove that super-symmetric operator must
have as an eigenvalue when the underlying bundle has odd rank
Decomposition, purity and fibrations by normal crossing divisors
We give a simple geometric proof of the decomposition theorem in terms of Thom-Whitney stratifications by reduction to fibrations by normal crossings divisors over the strata and explain the relation with the local purity theorem an unpublished result of Deligne and Gabber