Related papers: Irregular Hodge filtration of some confluent hyper…
We introduce the notion of mixed Hodge complex on an algebraic variety, improving Du Bois' filtered complex, and relate Deligne's theory of mixed Hodge structure with the theory of mixed Hodge module. This was supposed to be true, but is…
On the space of homomorphisms from a Verma module to an indecomposable tilting module of the BGG-category O we define a natural filtration following Andersen and establish a formula expressing the dimensions of the filtration steps in terms…
This is partly a survey article on nonabelian Hodge theory, but we also give proofs of results that have only been announced elsewhere. In the introduction we discuss a wide range of recent work on this subject and give some references. In…
We survey a theory of limits of polarizable variations of real Hodge structure in the quasi-unipotent monodromy case using the V-filtration of Kashiwara and Malgrange indexed by rational numbers, which does not necessarily seem familiar to…
We employ the inductive structure of determinantal varieties to calculate the mixed Hodge module structure of local cohomology modules with determinantal support. We show that the weight of a simple composition factor is uniquely determined…
We study Fourier transforms of holonomic D-modules on the complex affine line and show that their enhanced solution complexes are described by a twisted Morse theory. We thus recover and even strengthen the well-known formula for their…
We prove that invariant subbundles of the Kontsevich-Zorich cocycle respect the Hodge structure. In particular, we establish a version of Deligne semisimplicity in this context. This implies that invariant subbundles must vary polynomially…
We study a natural Hodge module on the Hilbert scheme of four points on affine three-space, which categorifies the Donaldson--Thomas invariant of the Hilbert scheme. We determine the weight filtration on the Hodge module explicitly in terms…
We extend previous work to the case of $\mathbb{Q}$-divisors. Namely, for certain parametrically prime holomorphic functions $f$ and $\alpha \geq 0$, we obtain an explicit expression for the Hodge filtration on…
We construct the limiting mixed Hodge structure of a degeneration of compact K\"ahler manifolds over the unit disk with a possibly non-reduced simple normal crossing singular central fiber via holonomic $\mathscr D$-modules, generalizing…
Based on the recent developments in the irregular Riemann-Hilbert correspondence for holonomic D-modules and the Fourier-Sato transforms for enhanced ind-sheaves, we study the Fourier transforms of some irregular holonomic D-modules. For…
Perverse-Hodge complexes are objects in the derived category of coherent sheaves obtained from Hodge modules associated with Saito's decomposition theorem. We study perverse-Hodge complexes for Lagrangian fibrations and propose a symmetry…
We consider the residual B-model variation of Hodge structure of Iritani defined by a family of toric Calabi--Yau hypersurfaces over a punctured disk $D \setminus \{ 0\}$. It is naturally extended to a logarithmic variation of polarized…
We study the Hodge filtration of the intersection cohomology Hodge module for toric varieties. More precisely, we study the cohomology sheaves of the graded de Rham complex of the intersection cohomology Hodge module and give a precise…
Unstable holomorphic bundles can be described algebraically by Harder-Narasimhan filtrations. In this note we show how such filtrations correspond to the existence of special metrics defined by Hermitian-Einstein inequalities.
Let $X$ be a smooth irreducible quasi-projective algebraic variety over a number field $K$. Suppose $X$ is equipped with a $p$-adic \'{e}tale local system compatible with an admissible graded-polarized variation of mixed Hodge structures on…
We introduce the intersection cohomology module of a matroid and prove that it satisfies Poincar\'e duality, the hard Lefschetz theorem, and the Hodge-Riemann relations. As applications, we obtain proofs of Dowling and Wilson's Top-Heavy…
This is a survey paper on the Riemann-Hilbert correspondence on (irregular) holonomic D-modules, based on the 16-th Takagi lecture (2015/11/28). In this paper, we use subanalytic sheaves, an analogous notion to the one of indsheaves.
We review Hodge structures, relating filtrations, Galois Theory and Jordan-Holder structures. The prototypical case of periods of Riemann surfaces is compared with the Galois-Artin framework of algebraic numbers.
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine plane monomial curve. We also describe the irregularity complex of such a system with respect to its…