Residues and filtered D-modules

@article{Schnell2010ResiduesAF,
  title={Residues and filtered D-modules},
  author={Christian Schnell},
  journal={Mathematische Annalen},
  year={2010},
  volume={354},
  pages={727-763}
}
  • C. Schnell
  • Published 4 May 2010
  • Mathematics
  • Mathematische Annalen
For an embedding of sufficiently high degree of a smooth projective variety X into projective space, we use residues to define a filtered holonomic $${\mathcal{D}}$$ -module $${(\mathcal{M}, F)}$$ on the dual projective space. This gives a concrete description of the intermediate extension to a Hodge module on P of the variation of Hodge structure on the middle-dimensional cohomology of the hyperplane sections of X. We also establish many results about the sheaves $${F_k{\mathcal{M}}}$$ , such… 
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References

SHOWING 1-10 OF 29 REFERENCES
The boundary behavior of cohomology classes and singularities of normal functions
In a family of projective complex algebraic varieties, all nonsingular fibers are topologically equivalent; in particular, their cohomology groups are isomorphic. Near the “boundary,” where the…
Complex analytic Néron models for arbitrary families of intermediate Jacobians
Given a family of intermediate Jacobians (for a polarizable variation of integral Hodge structure of odd weight) on a Zariski-open subset of a complex manifold, we construct an analytic space that…
VANISHING CYCLE SHEAVES OF ONE-PARAMETER SMOOTHINGS AND QUASI-SEMISTABLE DEGENERATIONS
We study the vanishing cycles of a one-parameter smoothing of a complex analytic space and show that the weight filtration on its perverse cohomology sheaf of the highest degree is quite close to the…
Algebraic D-modules
Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent,…
A remark on singularities of primitive cohomology classes
Green and Griffiths have introduced several notions of singularities associated with normal functions, especially in connection with middle dimensional primitive Hodge classes. In this note, by using…
Local Duality and Polarized Hodge Modules
We find a relationship between the graded quotients of a filtered holonomic D-module, their duals as coherent sheaves, and the characteristic variety, in case the filtered D-module underlies a…
Generic vanishing filtration and perverse objects in derived categories of coherent sheaves
This is a mostly expository paper, intended to explain a very natural relationship between two a priori distinct notions appearing in the literature: Generic Vanishing in the context of vanishing…
Onb-function, spectrum and rational singularity
by duality [18], because R~Tr,CCy, = 0 for i > 0 by [6, 31] (this follows also from [13, 21, 23]) where rc is assumed projective. Here COy denotes the dualizing sheaf (i.e., the dualizing complex…
On singularities of primitive cohomology classes
Green and Griffiths have introduced several notions of singularities associated with normal functions, especially in connection with middle-dimensional primitive Hodge classes. In this paper, by…
Singularities of admissible normal functions
In a recent paper, M. Green and P. Griffiths used R. Thomas’ work on nodal hypersurfaces to sketch a proof of the equivalence of the Hodge conjecture and the existence of certain singular admissible…
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