The perverse filtration and the Lefschetz Hyperplane Theorem
By M. A. Cataldo, L. Migliorini. 2008
78 citations recorded by the source corpus.
The perverse filtration in cohomology and in cohomology with compact supports is interpreted in terms of kernels of restrictions maps to suitable subvarieties by using the Lefschetz hyperplane theorem and spectral objects. Various mixed-Hodge-theoretic consequences for intersection cohomology and for the decomposition theorem are derived.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/23200913320d2306322eb3f1649d17663c0fa2d2
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In Computational Theory and Mathematics
In Geometry and Topology
- M. A. Cataldo
- L. Migliorini
- Claire Voisin
- Tamás Hausel
- D. Arapura
- T. Mochizuki
- Charles Vial
- Davesh Maulik
In Mathematical Physics
- M. A. Cataldo
- L. Migliorini
- Claire Voisin
- Tamás Hausel
- D. Arapura
- T. Mochizuki
- Charles Vial
- Davesh Maulik
Citations in the corpus
- The decomposition theorem, perverse sheaves and the topology of algebraic maps (2007, methodology): “More precisely, the results for projective varieties and the maps between them (in this case, all Hodge structures are pure) are found in [51, 54] and the extension to quasi projective varieties and the proper maps between them is found in [45], which builds heavily on [55].”