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De Rham complex of a Gerstenhaber algebra

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 Added by Vadim Schechtman
 Publication date 2015
  fields
and research's language is English




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We introduce a notion of the De Rham complex of a Gerstenhaber algebra which produces a notion of a quasi-BV structure, and allows to classify these structures, generalizing the classical results for polyvector fields.



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143 - Hongshan Li 2018
We will prove a Kodaira-Nakano type of vanishing theorem for the logarithmic de Rham complex of unitary local system. We will then study the weight filtration on the logarithmic de Rham complex, and prove a stronger statement for the associated graded complex.
In this paper we determine the motivic class---in particular, the weight polynomial and conjecturally the Poincare polynomial---of the open de Rham space, defined and studied by Boalch, of certain moduli of irregular meromorphic connections on the trivial bundle on $mathbb{P}^1$. The computation is by motivic Fourier transform. We show that the result satisfies the purity conjecture, that is, it agrees with the pure part of the conjectured mixed Hodge polynomial of the corresponding wild character variety. We also identify the open de Rham spaces with quiver varieties with multiplicities of Yamakawa and Geiss--Leclerc--Schroer. We finish with constructing natural complete hyperkahler metrics on them, which in the $4$-dimensional cases are expected to be of type ALF.
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