Related papers: Hypergeometric Hodge modules

The purpose of this paper is to study certain notions of metric positivity for the lowest nonzero piece in the Hodge filtration of a Hodge module. We show that the Hodge metric satisfies the minimal extension property. In particular, this…

Peter Scholze has raised the question whether some variant of the $q$-de Rham complex is already defined over the Habiro ring $\mathcal H = \lim_{m\in\mathbb N}\mathbb Z[q]_{(q^m-1)}^\wedge$. We show that such a variant exists whenever the…

We introduce several families of filtrations on the space of vector bundles over a smooth projective variety. These filtrations are defined using the large k asymptotics of the kernel of the Dolbeault Dirac operator on a bundle twisted by…

We investigate a relationship between a particular class of two-dimensional integrable non-linear $\sigma$-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the $\lambda$-deformed $G/G$…

We introduce mixed twistor $D$-modules, and establish the fundamental functorial property. We also prove that they are described as the gluing of admissible variations of mixed twistor structure. In a sense, mixed twistor $D$-modules could…

We introduce the notion of filtered perversity of a filtered differential complex on a complex analytic manifold $X$, without any assumptions of coherence, with the purpose of studying the connection between the pure Hodge modules and the…

To any complex algebraic variety endowed with a morphism to a complex affine torus we associate multivariable cohomological Alexander modules, and define natural mixed Hodge structures on their maximal Artinian submodules. The key…

Let $R$ be a commutative noetherian ring. Enochs and Huang [EH] proved that over a Gorenstein ring of Krull dimension $d$, every Gorenstein injective module admits a finite filtration of Gorenstein injective submodules. In this paper, we…

This text is an expository survey on the interplay between polarized variation of Hodge structure (PVHS) and the formalism of Hodge modules. We specifically review the extensions of a PVMHS over their singularities and its relation to mixed…

We study the Hodge filtration on the local cohomology sheaves of a smooth complex algebraic variety along a closed subscheme Z in terms of log resolutions, and derive applications regarding the local cohomological dimension, the Du Bois…

In this paper we are interested in proving that the infinitesimal variations of Hodge structure of hypersurfaces of high enough degree lie in a proper subvariety of the variety of all infinitesimal variations. This is proved using a space…

It is well known that numerical quantities arising from the theory of D-modules are related to invariants of singularities in birational geometry. This paper surveys a deeper relationship between the two areas, where the numerical…

Hodge-filtered derived de Rham cohomology of a ring $R$ can be described (up to completion and shift) as the graded pieces of the even filtration on $\mathrm{HC}^-(R)$. In this paper we show a deformation of this result: If $R$ admits a…

A Lefschetz module is a module over a graded algebra $A$ that satisfies analogues of Poincar\'{e} duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to an open convex cone $\mathscr{K}$ in the degree one…

We show that very general hypersurfaces in odd-dimensional simplicial projective toric varieties verifying a certain combinatorial property satisfy the Hodge conjecture (these include projective spaces). This gives a connection between the…

Let $\mathcal{O}_K$ be a complete discrete valuation ring of mixed characteristic $(0,p)$ with perfect residue field. We prove the existence of the Hodge-Newton filtration for $p$-divisible groups over $\mathcal{O}_K$ with additional…

We prove that $\mathrm{SO}(3)$ modular functors in genus $0$ have geometric origin and support integral variations of Hodge structures for any odd level $r$ and $r$-th root of unity $\zeta_r\in\mathbb{C}$. We identify the TQFT intersection…

We give a proof of the Thom-Sebastiani type theorem for holonomic filtered $D$-modules satisfying certain good conditions (including Hodge modules) by using algebraic partial microlocalization. By a well-known relation between multiplier…

Let $G/H$ be a homogeneous variety, and let $X$ be a $G$-equivariant embedding of $G/H$such that the number of $G$-orbits in $X$ is finite. We show that the equivariant Borel-Moore homology of $X$ has a filtration with associated graded…

In mixed characteristic and in equal characteristic $p$ we define a filtration on topological Hochschild homology and its variants. This filtration is an analogue of the filtration of algebraic $K$-theory by motivic cohomology. Its graded…