Related papers: On the Hitchin morphism for higher dimensional var…

We study resolutions of the rational map to the moduli space of stable curves that associates with a point in the Hitchin base the spectral curve. In the rank two case the answer is given in terms of the space of quadratic multi-scale…

We prove a Hitchin-Kobayashi correspondence for extensions of Higgs bundles. The results generalize known results for extensions of holomorphic bundles. Using Simpson's methods, we construct moduli spaces of stable objects. In an appendix…

We show the smoothness over the affine line of the Hodge moduli space of logarithmic t-connections of coprime rank and degree on a smooth projective curve with geometrically integral fibers over an arbitrary Noetherian base. When the base…

We extend the holographic construction from AdS3 to higher dimensions. In particular, we show that the Bekenstein-Hawking entropy of codimension-two surfaces in the bulk with planar symmetry can be evaluated in terms of the 'differential…

For $S$ a closed surface of genus $g\geq2$, we construct a canonical diffeomorphism from the degree $3$ Fock-Thomas space $\mathcal{T}^3(S)$ of higher complex structures to the $\text{SL}(3,\mathbb{R})$ Hitchin component. Our construction…

In this paper, we present an algebro-geometric construction of the Hitchin connection in the parabolic setting for a fixed determinant line bundle. Our strategy is based on Hecke modifications, where we provide a decomposition formula for…

It was shown by Diaconescu, Donagi and Pantev that Hitchin systems of type ADE are isomorphic to certain Calabi-Yau integrable systems. In this paper, we prove an analogous result in the setting of meromorphic Hitchin systems of type A…

This work investigates edge modes in non-Hermitian photonic crystals with broken spectral reciprocity. In such systems, the spectra of the underlying operators generally form closed loops over the complex plane with nontrivial spectral…

In this paper, we study the geometric and dynamical properties of maximal representations of surface groups into Hermitian Lie groups of rank 2. Combining tools from Higgs bundle theory, the theory of Anosov representations, and…

We give a characterisation of Atiyah's and Hitchin's transverse Hilbert schemes of points on a symplectic surface in terms of bi-Poisson structures. Furthermore, we describe the geometry of hyperk\"ahler manifolds arising from the…

We prove analogues of several well-known results concerning rational morphisms between quadrics for the class of so-called quasilinear $p$-hypersurfaces. These hypersurfaces are nowhere smooth over the base field, so many of the geometric…

We construct some analog of cubical Bloch's higher Chow groups. Instead of considering cycles in $X\times\mathbb A^n$ we consider varieties $Y$ over $X$ together with a distinguished element in the $n$-th exterior power of the…

We develop the theory of d-holomorphic connections on d-holomorphic vector bundles over a Klein surface by constructing the analogous Atiyah exact sequence for d-holomorphic bundles. We also give a criterion for the existence of…

We give a complete, self-contained computation of the spectral data parametrising Higgs bundles in the generic fibres of the $\mathrm{SO}_{2n+1}$-Hitchin fibration where the Higgs fields are $L$-twisted endomorphisms. Although the spectral…

By means of a certain exact non-abelian duality transformation, we show that there is a natural embedding, dense in the sense of the distributions in the large-N limit, of parabolic Higgs bundles of rank N on a fiber two-dimensional torus…

A generalized Hitchin equation was proposed as the BPS equation for a large class of four dimensional N=1 theories engineered using M5 branes. In this paper, we show how to write down the spectral curve for the moduli space of generalized…

Any irreducible Dynkin diagram $\Delta$ is obtained from an irreducible Dynkin diagram $\Delta_h$ of type $\mathrm{ADE}$ by folding via graph automorphisms. For any simple complex Lie group $G$ with Dynkin diagram $\Delta$ and compact…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…

We establish an upper bound for the cochain type level of the total space of a pull-back fibration. It explains to us why the numerical invariant for a principal bundle over the sphere are less than or equal to two. Moreover computational…

We study finite morphisms of varieties and the link between their top multiplicity loci under certain assumptions. More precisely, we focus on how to determine that link in terms of the spaces of arcs of the varieties.