Related papers: On the Hitchin morphism in positive characteristic

In a previous paper, \cite{Berndtsson}, we have studied a property of subharmonic dependence on a parameter of Bergman kernels for a family of weighted $L^2$-spaces of holomorphic functions. Here we prove a result on the curvature of a…

We generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler…

Let G be a connected complex reductive affine algebraic group, and let K be a maximal compact subgroup. Let X be a compact connected K\"ahler manifold whose fundamental group Gamma is virtually nilpotent. We prove that the character variety…

We review and study the notion of Higgs Grassmannians, which are schemes parametrizing the Higgs subbundles of a given Higgs bundle over a smooth variety. We write their equations as closed subschemes of the usual Grassmann bundles and…

We analyze and completely describe the four cases when the Hitchin fibration on a $2$-dimensional moduli space of irregular Higgs bundles over $\mathbb{C}P^{1}$ has a single singular fiber. The case when the fiber at infinity is of type…

We establish that the isomorphy type as an abstract algebraic variety of the complement of an ample hyperplane sub-bundle H of a projective space bundle of rank r-1 over the projective line depends only on the the r-fold self-intersection…

We provide a geometric construction of the unitary structure which is projectively preserved by the Hitchin connection. We analyze the asymptotic behavior of it and we establish that it is uniformly in the level equivalent to the Hermitian…

We demonstrate the construction of Poisson structures via Lie algebroids on moduli spaces of twisted stable Higgs bundles over stacky curves. The construction provides new examples of Poisson structures on such moduli spaces. Special…

We review some results and techniques from our papers devoted to the computation of motivic classes of stacks of parabolic Higgs budles and bundles with connections on a curve. In the last section we present some directions for future work,…

In this paper the moduli space of Higgs pairs over a fixed smooth projective curve with extra formal data is defined and it is endowed with a scheme structure. We introduce a relative version of the Krichever map using a fibration of Sato…

We study the Hitchin map for $G_{\mathbb{R}}$-Higgs bundles on a smooth curve, where $G_{\mathbb{R}}$ is a quasi-split real form of a complex reductive algebraic group $G$. By looking at the moduli stack of regular $G_{\mathbb{R}}$-Higgs…

Given a smooth projective complex curve $X$ with an involution $\sigma$, we study the Hitchin systems for the locus of anti-invariant (resp. invariant) stable vector bundles over $X$ under $\sigma$. Using these integrable systems and the…

This is a review article on some applications of generalised parabolic structures to the study of torsion free sheaves and $L$-twisted Hitchin pairs on nodal curves. In particular, we survey on the relation between representations of the…

We look at rank two parabolic Higgs bundles over the projective line minus five points which are semistable with respect to a weight vector $\mu\in[0,1]^5$. The moduli space corresponding to the central weight $\mu_c=(\frac{1}{2}, \dots,…

We show how to construct in an elementary way the invariant of the KHK discretisation of a cubic Hamiltonian system in two dimensions. That is, we show that this invariant is expressible as the product of the ratios of affine polynomials…

Kontsevich's characteristic classes are invariants of framed smooth fiber bundles with homology sphere fibers. It was shown by Watanabe that they can be used to distinguish smooth $S^4$-bundles that are all trivial as topological fiber…

We prove a closed formula counting semistable twisted Higgs bundles of fixed rank and degree over a smooth projective curve defined over a finite field. We also prove a formula for the Donaldson-Thomas invariants of the moduli spaces of…

Let $\{{\cdot},{\cdot}\}_{\boldsymbol{\mathcal{P}}}$ be a variational Poisson bracket in a field model on an affine bundle $\pi$ over an affine base manifold $M^m$. Denote by $\times$ the commutative associative multiplication in the…

Let $C$ be a smooth projective curve of genus $g$ over a finite field $\mathbb{F}_q$ and let $D$ be a divisor on $C$ of degree $>2g-2$. We assume that the characteristic of $\mathbb{F}_q$ is sufficiently large. Let $n$ be an integer and let…

An effective family of spectral curves appearing in Hitchin fibrations is determined. Using this family the moduli spaces of stable Higgs bundles on an algebraic curve are embedded into the Sato Grassmannian. We show that the Hitchin…