相关论文: Higgs bundles, abelian gerbes and cameral data

We define the Toledo invariant of a G-Higgs bundle on a Riemann surface, where G is a real semisimple group of Hermitian type, and we prove a Milnor-Wood type bound for this invariant when the bundle is semistable. We prove rigidity results…

The spectral side of the (conjectural) Betti geometric Langlands correspondence concerns sheaves on the character stack of an algebraic curve; in particular, the categories in question are manifestly invariant under deformations of the…

We study three instability stratifications of the stack of twisted Higgs bundle of a fixed rank and degree on a smooth complex projective curve. The first is the Harder-Narasimhan (HN) stratification, defined by the instability type of the…

Let $X$ be a compact Riemann surface of genus $g \geq 2$, and let $D \subset X$ be a fixed finite subset. We prove the semiprojectivity of the moduli space of semistable symplectic or orthogonal parabolic Higgs bundles over $X$. We show…

Let $X$ be a compact Riemann surface. Let $(E,\theta)$ be a stable Higgs bundle of degree $0$ on $X$. Let $h_{\det(E)}$ denote a flat metric of the determinant bundle $\det(E)$. For any $t>0$, there exists a unique harmonic metric $h_t$ of…

Let T be the one-dimensional complex torus. We consider the action of an automorphism of a Riemann surface X on the cohomology of the T-equivariant determinant line bundle over the moduli space of rank two Higgs bundles on X with fixed…

Let $X$ be a smooth complex projective curve of genus $g$ and let $L$ be a line bundle on $X$ with $\mathrm{deg}\,L>0$. Let $\mathbf{M}$ be the moduli space of semistable rank 2 $L$-twisted Higgs bundles with trivial determinant on $X$. Let…

We study mirror symmetry on the singular locus of the Hitchin system at two levels. Firstly, by covering it by (supports of) $(BBB)$-branes, corresponding to Higgs bundles reducing their structure group to the Levi subgroup of some…

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 $(E,\overline{\partial}_E,\theta)$ be a stable Higgs bundle of degree $0$ on a compact connected Riemann surface. Once we fix the flat metric $h_{\det(E)}$ on the determinant of $E$, we have the harmonic metrics $h_t$ $(t>0)$ for the…

Let $G$ be a simply connected semisimple group over $\mathbb{C}$. We show that a certain involution of an open subset of the affine Grassmannian of $G$, defined previously by Achar and the author, corresponds to the action of the nontrivial…

We study the locus of the moduli space of Higgs bundles on a curve given by those Higgs bundles obtained by pushforward under an unramified cover. We equip these loci with a hyperholomorphic bundle so that they can be viewed as BBB-branes,…

We define Hitchin's moduli space for a principal bundle $P$, whose structure group is a compact semisimple Lie group $K$, over a compact non-orientable Riemannian manifold $M$. We use the Donaldson-Corlette correspondence, which identifies…

Prior works relating meromorphic Higgs bundles to topological recursion, in particular those of Dumitrescu-Mulase, have considered non-singular models that allow the recursion to be carried out on a smooth Riemann surface. We start from an…

Relying on a notion of "numerical effectiveness" for Higgs bundles, we show that the category of "numerically flat" Higgs vector bundles on a smooth projective variety $X$ is a Tannakian category. We introduce the associated group scheme,…

Let G be a Lie supergroup and H a closed subsupergroup. We study the unimodularity of the homogeneous supermanifold G/H, i.e. the existence of G-invariant sections of its Berezinian line bundle. To that end, we express this line bundle as a…

Using Morse-theoretic techniques, we show that the moduli space of U*(2n)-Higgs bundles over a compact Riemann surface is connected.

In this paper we study four families of moduli problems which give rise to two dimensional examples of the Hitchin map. Using a few Fourier-Mukai transforms on the corresponding spectral curves, we give isomorphisms between these moduli…

These notes have been prepared as reading material for the mini-course given by the author at the "2019 Graduate Summer School" at Park City Mathematics Institute - Institute for Advanced Study. We begin by introducing Higgs bundles and…

We introduce the moduli space of quasi-parabolic $SL(2,\mathbb{C})$-Higgs bundles over a compact Riemann surface $\Sigma$ and consider a natural involution, studying its fixed point locus when $\Sigma$ is $\mathbb{C} \mathbb{P}^1$ and…