On the Hodge Filtration of Hodge Modules
نویسندگان
چکیده
منابع مشابه
On the Hodge Filtration of Hodge Modules
Let X be a complex manifold, and Z an irreducible closed analytic subset. We have the polarizable Hodge Module ICZQ H whose underlying perverse sheaf is the intersection complex ICZQ. See [16]. Let (M,F ) be its underlying filtered DX -Module. ThenM is the unique regular holonomic DX -Module which corresponds to ICZC by the Riemann-Hilbert correspondence [9] [13], and it is relatively easy to d...
متن کاملThe Hodge filtration on nonabelian cohomology
Whereas usual Hodge theory concerns mainly the usual or abelian cohomology of an algebraic variety—or eventually the rational homotopy theory or nilpotent completion of π1 which are in some sense obtained by extensions—nonabelian Hodge theory concerns the cohomology of a variety with nonabelian coefficients. Because of the basic fact that homotopy groups in higher dimensions are abelian, and si...
متن کاملDefinition of Pure Hodge Modules
(3) A good filtration F•M by OX -coherent subsheaves of M, such that FpM · FkD ⊂ Fp+kM and such that gr• M is coherent over gr• DX ' Sym • TX . Its Tate twist is defined by M(k) = (M, F•−kM,K ⊗Q Q(k)) where Q(k) = (2πi)Q ⊂ C. For a given function f : X → C, we want to define the nearby and vanishing cycles, denoted ψf and φf , in the category of filtered regular holonomic D-modules with Q-struc...
متن کاملFrobenius modules and Hodge asymptotics
We exhibit a direct correspondence between the potential defining the H small quantum module structure on the cohomology of a Calabi-Yau manifold and the asymptotic data of the A-model variation of Hodge structure. This is done in the abstract context of polarized variations of Hodge structure and Frobenius modules.
متن کاملWeak Positivity for Hodge Modules
We prove the weak positivity of the kernels of Kodaira-Spencertype maps for pure Hodge module extensions of generically defined variations of Hodge structure.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Moscow Mathematical Journal
سال: 2009
ISSN: 1609-3321,1609-4514
DOI: 10.17323/1609-4514-2009-9-1-151-181