Polarizable twistor D-modules
By C. Sabbah. 2005
130 citations recorded by the source corpus.
We prove a Decomposition Theorem for the direct image of an irreducible local system on a smooth complex projective variety under a morphism with values in another smooth complex projective variety. For this purpose, we construct a category of polarized twistor D-modules and show a Decomposition Theorem in this category.
Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/5ea31846cb6adab640144323efa58325f4743adb
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In Atomic and Molecular Physics, and Optics
In Electrical and Electronic Engineering
Citations in the corpus
- Local Systems on Proper Algebraic V -manifolds (2010, methodology): “The variation of twistor structure on L corresponds to a prefered section of the twistor moduli stack MDH(X,GL(n)), and the above complex is the Deligne-Hitchin glueing of the complexes calculating cohomology of λ-connections on X and X, see [87] [99].”
- Mixed Twistor D-modules (2011, methodology): “Let us recall the following isomorphism from [45] and [48].”
- The decomposition theorem, perverse sheaves and the topology of algebraic maps (2007, unknown): “Sabbah, [143] and T.”
- Katz's middle convolution algorithm (2006, background): “It would be good to have the full middle-convolution theory for the general setup of parabolic logarithmic λ-connections [107] [108] [109] [122].”
- Hodge theoretic aspects of mirror symmetry (2008, background): “• Various versions of the notion of a (complex,polarized) nc-Hodge structure appear in algebraic geometry and non-abelian Hodge theory in the works of Simpson [Sim97a, Sim97b] and T.Mochizuki [Moc06a, Moc06b, Moc07a, Moc07b] under the names of (tame or wild) harmonic bundle or pure twistor structure”
- Hodge theoretic aspects of mirror symmetry (2008, background): “Sabbah [Sab05b] under the name integrable pure twistor D-module.”
- Kobayashi-Hitchin correspondence for tame harmonic bundles II (2006, methodology): “z E;F;r/ (see Sabbah [16], for example), we can derive the existence of the Corlette–Jost–Zuo metric from Theorem 1.”