Related papers: A Non-Linear Deformation of the Hitchin Dynamical …

We determine the non-reduced components of global nilpotent cones in various cases of interest. In particular, under the appropriate coprimality conditions, we show: (1) the global nilpotent cone for an $L$-twisted…

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…

We study moduli spaces of sheaves over non-projective K3 surfaces. More precisely, if $v=(r,\xi,a)$ is a Mukai vector on a K3 surface $S$ with $r$ prime to $\xi$ and $\omega$ is a "generic" K\"ahler class on $S$, we show that the moduli…

Let M(v) be the moduli of stable sheaves on K3 surfaces X of Mukai vector v. If v is primitive, than it is expected that M(v) is deformation equivalent to some Hilbert scheme and weight two hogde structure can be described by H^*(X,Z).…

Let X be a smooth projective curve over a field of characteristic p>0. We show that the Hitchin morphism, which associates to a Higgs bundle its characteristic polynomial, has a non-trivial deformation over the affine line. This deformation…

In this paper, we show the moduli spaces of stable sheaves on K3 surfaces are irreducible symplectic manifolds, if the associated Mukai vectors are primitive. More precisely, we show that they are related to the Hilbert scheme of points. We…

The Hitchin morphism is a map from the moduli space of Higgs bundles $\mathscr{M}_X$ to the Hitchin base $\mathscr{B}_X$, where $X$ is a smooth projective variety. When $X$ has dimension at least two, this morphism is not surjective in…

For the moduli space of Higgs bundles on a Riemann surface of positive genus, critical points of the natural Morse-Bott function lie along the nilpotent cone of the Hitchin fibration and are representations of $\mbox{A}$-type quivers in a…

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…

Motivated by the connection to 4d $\mathcal{N}=2$ theories, we study the global behavior of families of tamely-ramified $SL_N$ Hitchin integrable systems as the underlying curve varies over the Deligne-Mumford moduli space of stable pointed…

Let X be a K3 surface and M a smooth and projective moduli space of stable sheaves on X of Mukai vector v. A universal sheaf U over X x M induces an integral transform F from the derived category D(X) of coherent sheaves on X to that on M.…

In this article, we construct a flat degeneration of the derived moduli stack of Higgs bundles on smooth curves using the stack of expanded degenerations of Jun Li. We show that there is an intrinsic relative log-symplectic form on the…

We study the nilpotent cone in the Mukai system for rank two and genus two. We compute the degrees and multiplicities of its irreducible components and describe their cohomology classes.

Let $X$ be a compact Riemann surface of genus $g \geq 2$, and let $D \subset X$ be a fixed finite subset. Let $\mathcal{M}(r,d,\alpha)$ denote the moduli space of stable parabolic $G$-bundles (where $G$ is a complex orthogonal or symplectic…

Components of the Moduli space of sheaves on a K3 surface are parametrized by a lattice; the (algebraic) Mukai lattice. Isometries of the Mukai lattice often lift to symplectic birational isomorphisms of the collection of components. An…

The Hitchin system is a completely integrable hamiltonian system (CIHS) on the cotangent space to the moduli space of semi-stable vector bundles over a curve. We consider the case of rank-two vector bundles with trivial determinant. Such a…

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…

Spectral transformation is known to set up a birational morphism between the Hitchin and Beauville-Mukai integrable systems. The corresponding phase spaces are: (a) the cotangent bundle of the moduli space of bundles over a curve C, and (b)…

Let X be a K3 surface with a polarization H of degree H^2=2rs and with a primitive Mukai vector (r,H,s). The moduli space of sheaves over X with the isotropic Mukai vector (r,H,s) is again a K3 surface Y. We prove that Y\cong X, if Picard…

In this paper we study deformation classes of moduli spaces of sheaves on a projective K3 surface. More precisely, let $(S1,H1)$ and $(S2,H2)$ be two polarized K3 surfaces, $m\in\mathbb{N}$, and for $i=1,2$ let $mv_{i}$ be a Mukai vector on…