Related papers: Generalized Deligne-Hitchin Twistor Spaces: Constr…
We generalize the construction of a moduli space of semistable pairs parametrizing isomorphism classes of morphisms from a fixed coherent sheaf to any sheaf with fixed Hilbert polynomial under a notion of stability to the case of projective…
It is known that generalized deformation in the sense of Hitchin-Gaultieri is a geometric realization of the degree-2 component of Kontsevich-Barannikov's homological approach to extended deformation. Through extended deformation, one…
We define two equivalent notions of twisted stable map from a curve to a Deligne-Mumford stack with projective moduli space, and we prove that twisted stable maps of fixed degree form a complete Deligne-Mumford stack with projective moduli…
We introduce a model for Hermitian holormorphic Deligne cohomology on a projective algebraic manifold which allows to incorporate singular hermitian structures along a normal crossing divisor. In the case of a projective curve, the…
We construct twisted Calogero-Moser (CM) systems with spins as the Hitchin systems derived from the Higgs bundles over elliptic curves, where transitions operators are defined by an arbitrary finite order automorphisms of the underlying Lie…
We study the hypersymplectic geometry of the moduli space of solutions to Hitchin's harmonic map equations on a $G$-bundle. This is the split-signature analogue of Hitchin's Higgs bundle moduli space. Due to the lack of definiteness, this…
We study the algebraic geometry of twisted Higgs bundles of cyclic type along complex curves. These objects, which generalize ordinary cyclic Higgs bundles, can be identified with representations of a cyclic quiver in a twisted category of…
We study how a gluing construction, which produces compact manifolds with holonomy G_2 from matching pairs of asymptotically cylindrical G_2-manifolds, behaves under deformations. We show that the gluing construction defines a smooth map…
In this paper, we study the moduli space of unipotent Weil-Deligne representations valued in a split reductive group $G$ and characterise which irreducible components are smooth. We apply the smoothness results proved to show that a certain…
In this paper, we shall generalize the theory of mixed Hodge structures due to Deligne and obtain a subcategory GMHS in the category of mixed Hodge structures such that we have Ext_{GMHS}^2(Q,-)\not=0 in general.
We study smooth higher symmetry groups and moduli $\infty$-stacks of generic higher geometric structures on manifolds. Symmetries are automorphisms which cover non-trivial diffeomorphisms of the base manifold. We construct the smooth higher…
We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an $SU(3)\times Spin(6+n)$ structure within…
In this lecture, we review some of the concepts of generalized geometry, as introduced by Hitchin and developed in the speaker's thesis. We also prove a Hodge decomposition for the twisted cohomology of a compact generalized K\"ahler…
We first make a little survey of the twistor theory for hypercomplex, generalized hypercomplex, quaternionic or generalized quaternionic manifolds. This last theory was iniated by Pantilie, who shows that any generalized almost quaternionic…
In the genus one case, we make explicit some constructions of Veech on flat surfaces and generalize some geometric results of Thurston about moduli spaces of flat spheres as well as some equivalent ones but of an analytico-cohomological…
We give an explicit geometric structures interpretation of the $G_2'$-Hitchin component $Hit(S, G_2') \subset \chi(\pi_1S,G_2')$ of a closed oriented surface $S$ of genus $g \geq 2$. In particular, we prove $Hit(S, G_2')$ is naturally…
It is shown that any irreducible analytic 1-flat $G$-structure as well as any analytic torsion-free affine connection with irreducibly acting holonomy group can, in principle, be contstructed by twistor methods.
We investigate the Hitchin hyperk\"ahler metric on the moduli space of strongly parabolic $\mathfrak{sl}(2,\C)$-Higgs bundles on the $n$-punctured Riemann sphere and its degeneration obtained by scaling the parabolic weights $t\alpha$ as…
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…
The moduli space of Higgs bundles can be constructed as a quotient of an infinite-dimensional space and hence admits an orbit type decomposition. In this paper, we show that the orbit type decomposition is a complex Whitney stratification…