Related papers: Compactifying the rank two Hitchin system via spec…

Let $(E,\theta)$ be a Higgs bundle of rank $2$ and degree $0$ on a compact Riemann surface $X$ whose spectral curve is smooth. The tangent space of the moduli space of Higgs bundles at $(E,\theta)$ is equipped with two natural metrics…

We study the compactification of the moduli space of a certain class of rank-two irregular connections on the Riemann sphere, presenting one double pole and two simple poles. To construct the compactification explicitly, we identify a class…

We study the parametrization of the moduli space Bun_2(C)_L of rank 2 bundles over a curve C with fixed determinant, provided by Hecke modifications at fixed points of the trivial bundle. This parametrization is closely related to the…

Let G be a split reductive group. We introduce the moduli problem of "bundle chains" parametrizing framed principal G-bundles on chains of lines. Any fan supported in a Weyl chamber determines a stability condition on bundle chains. Its…

We introduce the notion of generalized hyperpolygon, which arises as a representation, in the sense of Nakajima, of a comet-shaped quiver. We identify these representations with rigid geometric figures, namely pairs of polygons: one in the…

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 continue the study of the rational Picard group of the moduli space of Hitchin's spectral covers started in P. Zograf's and D. Korotkin's work [11]. In the first part of the paper we expand the ``boundary'', ``Maxwell stratum'' and…

We review recent work on the compactification of the moduli space of Hitchin's self-duality equation. We study the degeneration behavior near the ends of this moduli space in a set of generic directions by showing how limiting…

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…

In this paper we study Hitchin system on singular curves. Some examples of such system were first considered by N. Nekrasov (hep-th/9503157), but our methods are different. We consider the curves which can be obtained from the projective…

The moduli space of stable vector bundles on a Riemann surface is smooth when the rank and degree are coprime, and is diffeomorphic to the space of unitary connections of central constant curvature. A classic result of Newstead and…

We prove that given a Hitchin representation in a real split rank 2 group $\mathsf G_0$, there exists a unique equivariant minimal surface in the corresponding symmetric space. As a corollary, we obtain a parametrization of the Hitchin…

We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for $GL_n$ over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of…

Let X be a nonsingular projective algebraic variety, and let S be a line bundle on X. Let A = (a_1,..., a_n) be a vector of integers. Consider a map f from a pointed curve (C,x_1,...,x_n) to X satisfying the following condition: the line…

We are interested in studying the variation of the Hitchin fibration in moduli spaces of parabolic Higgs bundles, under the action of a ramified covering. Given a degree two map $\pi$ : Y $\rightarrow$ X between compact Riemann surfaces, we…

We introduce a general abstract notion of fine compactified Jacobian for nodal curves of arbitrary genus. We focus on genus 1 and prove combinatorial classification results for fine compactified Jacobians in the case of a single nodal curve…

We generalize Bertram's work on rank two vector bundles to an irreducible projective nodal curve C. We use extensions of a line bundle L by O_C and the associated `forgetful' map to study a compactification of the moduli space of…

Given a smooth curve with weighted marked points, the Abel-Jacboi map produces a line bundle on the curve. This map fails to extend to the full boundary of the moduli space of stable pointed curves. Using logarithmic and tropical geometry,…

We construct new compactifications with good properties of moduli spaces of maps from nonsingular marked curves to a large class of GIT quotients. This generalizes from a unified perspective many particular examples considered earlier in…

The paper aims at giving an introduction to the notion of quantum curves. The main purpose is to describe the new discovery of the relation between the following two disparate subjects: one is the topological recursion, that has its origin…