Related papers: Twistor space for local systems on an open curve

We consider normal almost contact structures on a Riemannian manifold and, through their associated sections of an ad-hoc twistor bundle, study their harmonicity, as sections or as maps. We rewrite these harmonicity equations in terms of…

It is shown that there exists a twistor space on the $n$-fold connected sum of complex projective planes $n\mathbb{CP}^2$, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic…

We have studied irreducible Hom-Lie algebroid connections for Hom-bundle and prove that the H-gauge theoretic moduli space has a Hausdorff Hilbert manifold structure. This work generalizes some known results about simple semi-connections…

The ADHM construction establishes a one-to-one correspondence between framed torsion free sheaves on the projective plane and stable framed representations of a quiver with relations in the category of complex vector spaces. This paper…

We construct a new compactification of the moduli space of maps from pointed nonsingular projective stable curves to a nonsingular projective variety with prescribed ramification indices at the points. It is shown to be a proper…

We give a sufficient criterion, which we call stability, for a coarse Lipschitz map $f$ from a complete manifold $X$ with Ricci curvature bounded below to a proper Hadamard space $Y$ to be within bounded distance of a harmonic map. We prove…

The enumerative geometry of r-th roots of line bundles is the subject of Witten's conjecture and occurs in the calculation of Gromov-Witten invariants of orbifolds. It requires the definition of the suitable compact moduli stack and the…

We prove that the moduli space of stable maps of degree 2 to the moduli space of rank 2 stable bundles of fixed determinant O(-x) over a smooth projective curve of genus g>2 has two irre- ducible components which intersect transversely. One…

We study the behavior of the Gieseker space of semistable torsion-free sheaves of rank r and fixed c_1, c_2 on a non-singular projective surface as the polarization varies. It is shown that the ample cone admits a locally finite chamber…

We extend T. Y. Thomas's approach to the projective structures, over the complex analytic category, by involving the $\rho$-connections. This way, a better control of the projective flatness is obtained and, consequently, we have, for…

A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…

In "Quantization of Hitchin's Integrable System and Hecke Eigensheaves", Beilinson and Drinfeld introduced the "very good" property for a smooth complex equidimensional stack. They prove that for a semisimple complex group G, the moduli…

This is a survey of old and new results on the problem when a compatible almost complex structure on a Riemannian manifold is a harmonic section or a harmonic map from the manifold into its twistor space. In this context, a special…

Let X and X' be compact Riemann surfaces of genus at least three. Let G and G' be nontrivial connected semisimple linear algebraic groups over C. If some components $M_{DH}^d(X,G)$ and $M_{DH}^{d'}(X',G')$ of the associated Deligne--Hitchin…

We consider the moduli space of semistable Higgs bundles on a smooth projective curve. Motivated by mirror symmetry, Hausel and Hitchin showed that over an open of the locus of smooth Hitchin fibers, the duality of Donagi-Pantev intertwines…

We use a variation of a classical construction of A. Hatcher to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension…

We prove that smooth, separated Deligne--Mumford stacks in mixed characteristic with quasi-projective coarse moduli space are global quotient stacks and satisfy the resolution property. This builds on work of Kresch and Vistoli and of…

We explicitly construct a symplectomorphism that relates magnetic twists to the invariant hyperk\"ahler structure of the tangent bundle of a Hermitian symmetric space. This symplectomorphism reveals foliations by (pseudo-) holomorphic…

For a semisimple Lie group $G$ with parabolic subgroups $Q\subset P\subset G$, we associate to a parabolic geometry of type $(G,P)$ on a smooth manifold $N$ the correspondence space $\Cal CN$, which is the total space of a fiber bundle over…

We define the notion of a parahoric group scheme $\mathcal G$ over a smooth projective curve, and formulate four conjectures on the structure of the stack of $\mathcal G$-bundles, which generalize to this case well-known results on…