Related papers: Nonabelian Kodaira-Spencer maps

We show that the almost complex Hodge number $h^{0,1}$ varies with different choices of almost K\"ahler metrics. This answers the almost K\"ahler version of a question of Kodaira and Spencer.

We survey recent advances in non-abelian Hodge theory in the "mixed" setting of non-proper algebraic varieties. We then describe how these tools are used to construct algebraic Shafarevich morphisms and prove a version of the linear…

We present two non-equivalent families of hierarchies of non-Abelian compatible maps and we provide their Lax pair formulation. These maps are associated with families of hierarchies of non-Abelian Yang-Baxter maps, which we provide…

The goal of our work is to construct a class of morphisms between two canonical line bundles on integral models of PEL Shimura varieties via Kodaira--Spencer maps, and explicitly compute such morphisms and their effects on the canonical…

An interesting theme in complex differential geometry is to find a correspondence between algebraic objects and differential geometric objects. One of the most attractive is the non-abelian Hodge theory of Simpson. In this paper, pursuing…

We present the explicit formulae relating Hopf maps with Wigner's little groups. They, particularly, explain simple action of group on a fiber for the first and second Hopf fibrations, and present most simplified form for the third one.…

In the wild nonabelian Hodge correspondence on curves, filtered Stokes G-local systems are regarded as the objects on the Betti side. In this paper, we demonstrate a construction of the moduli space of them, called the Betti moduli space,…

In this continuation of \cite{BK} we investigate the non-abelian Hodge correspondence on compact Sasakian manifolds with emphasis on the quasi-regular case. On quasi-regular Sasakian manifolds, we introduce the notions of quasi-regularity…

We consider Abel maps for regular smoothing of nodal curves with values in the Esteves compactified Jacobian. In general, these maps are just rational, and an interesting question is to find an explicit resolution. We translate this problem…

This paper provides a description of an algebraic setting for the Lagrangian formalism over graded algebras and is intended as the necessary first step towards the noncommutative C-spectral sequence (variational bicomplex). A noncommutative…

The purpose of this paper is to construct non-trivial elements in the Abel-Jacobi kernels in any codimension by specializing correspondences with non-trivial Hodge-theoretical invariants at points with different transcendence degrees over a…

We prove the non-abelian Poincare lemma in higher gauge theory in two different ways. The first method uses a result by Jacobowitz which states solvability conditions for differential equations of a certain type. The second method extends a…

Let $E/F$ be an extension of number fields with $\mathrm{Gal}(E/F)$ simple and nonabelian. In [G] the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of $\mathrm{GL}_2$ along…

We construct a map between Bloch's higher Chow groups and Deligne homology for smooth, complex quasiprojective varieties on the level of complexes. For complex projective varieties this results in a formula which generalizes at the same…

We describe in simple geometric terms the Hodge filtration on the cohomology groups of the complement U in the projective plane of a curve C with ordinary double and triple points. Relations to Milnor algebra, syzygies of the Jacobian ideal…

A classification, according to invariant theory, of non-constant invariant Abel ODEs known as solvable and found in the literature is presented. A set of new integrable classes depending on one or no parameters, derived from the analysis of…

Let $\mathcal {A}$ be a finitary hereditary abelian category. In this note, we use the associativity of the derived Hall algebra associated to the bounded derived category of $\mathcal {A}$, whose multiplication structure constants are…

We define a pro-$p$ Abelian sheaf on a modular curve of a fixed level $N \geq 5$ divisible by a prime number $p \neq 2$. Every $p$-adic representation of $\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ associated to an eigenform is obtained…

In this paper, we explore a notion of nonabelian Hodge structure on the fundamental group of an algebraic variety. This is approach is compared to some alternative approaches due to Morgan, Hain and others. We also give criteria for a…

We use Getzler's Gauss-Manin connection to prove the invariance of periodic cyclic cohomology for the smooth deformation of noncommutative tori. We explicitly calculate the parallel translation maps and use them to describe the behavior of…