相关论文: The mixed Hodge structure on the fundamental group…

We associate a family of ideal sheaves to any Q-effective divisor on a complex manifold, called higher multiplier ideals, using the theory of mixed Hodge modules and V-filtrations. This family is indexed by two parameters, an integer…

We define and construct mixed Hodge structures on real schematic homotopy types of complex projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. We also show that these split on…

The formal algebraic structures that govern higher-spin theories within the unfolded approach turn out to be related to an extension of the Kontsevich Formality, namely, the Shoikhet-Tsygan Formality. Effectively, this allows one to…

This note is inspired by the work of Deligne on the local behavior of Hodge structures at infinity. We study limit mixed Hodge structures of degenerating families of compact hyperk\"ahler manifolds. We show that when the monodromy action on…

We study collections of subrings of $H^*(\overline{\mathcal{M}}_{g,n})$ that are closed under the tautological operations that map cohomology classes on moduli spaces of smaller dimension to those on moduli spaces of larger dimension and…

Let k be a commutative algebra with the field of the rational numbers included in k and let (E,p,i) be a cleft extension of A. We obtain a new mixed complex, simpler than the canonical one, giving the Hochschild and cyclic homologies of E…

We determine the second fundamental form of a variation of Hodge Structure of a smooth projective hypersurface using the classical identification of the Hodge structure and the action of the infinitesimal variation of Hodge structure with…

Multiplicative Hitchin systems are analogues of Hitchin's integrable system based on moduli spaces of G-Higgs bundles on a curve C where the Higgs field is group-valued, rather than Lie algebra valued. We discuss the relationship between…

Let R be the connected component of the identity of the variety of representations of a finitely generated nilpotent group N into a connected reductive complex affine algebraic group G. We determine the mixed Hodge structure on the…

In this paper we give some evidence for the Tate (and Hodge) conjecture(s) for a class of Hilbert modular fourfolds X, whose connected components arise as arithmetic quotients of the fourfold product of the upper half plane by congruence…

In this article we are interested in morphisms without slope for mixed Hodge modules. We first show the commutativity of iterated nearby cycles and vanishing cycles applied to a mixed Hodge module in the case of a morphism without slope.…

This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian…

In this note, we give several equivalent characterizations of higher Du Bois and higher rational singularities in the context of globally defined hypersurfaces. As a key input, we characterize these singularities using the Hodge filtration…

We explain the theory of refined cycle maps associated to arithmetic mixed sheaves. This includes the case of arithmetic mixed Hodge structures, and is closely related to work of Asakura, Beilinson, Bloch, Green, Griffiths, Mueller-Stach,…

We show, for all $n\ge 2$ even and $d\ge 2+\frac{4}{n}$, that the moduli of smooth degree $d$ hypersurfaces of $\mathbb{P}^{n+1}$ contains infinitely many different Hodge loci whose Zariski tangent space has the same codimension as the…

The results of this paper can be divided into two parts, geometric and arithmetic. Let $X$ be a smooth projective curve over $\mathbb{C}$, and $e,\infty\in X(\mathbb{C})$ be distinct points. Let $L_n$ be the mixed Hodge structure of…

Higher order automorphic forms have recently been introduced to study important questions in number theory and mathematical physics. We investigate the connection between these functions and Chen's iterated integrals. Then using Chen's…

Based on the computation of the third author we obtain an interpretation of the third Mac Lane cohomology of rings using certain kind of crossed extensions of rings in the quadratic world. Actually we obtain two such interpretations…

The purpose of this work is to geometrize the notion of mixed Hodge structure. Therefore, we associate equivariant vector bundles on the projective plane to trifiltered vector spaces. Making this Rees construction with filtrations arising…

We study the geometry of the moduli space of planes in a general cubic 5-fold and its deformation. We show that this moduli space is a smooth projective surface whose canonical bundle is ample. We also show that the variation of degree 1…