Related papers: Relative regular Riemann-Hilbert correspondence

Let $M, M'$ be smooth, real analytic hypersurfaces of finite type in ${\mbf C^n}$ and $\h f$ a holomorphic correspondence (not necessarily proper) that is defined on one side of $M$, extends continuously up to $M$ and maps $M$ to $M'$. It…

This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…

We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We complete the local classification of normal holonomies for complex submanifolds. We show that the normal…

A Riemann-Hilbert problem for a $q$-difference Painlev\'e equation, known as $q\textrm{P}_{\textrm{IV}}$, is shown to be solvable. This yields a bijective correspondence between the transcendental solutions of $q\textrm{P}_{\textrm{IV}}$…

Let $K$ be any field, and let $E$ be any graph. We explicitly construct the projective resolution of simple left modules over the Leavitt path algebra $L_K(E)$ associated to cycles and irreducible polynomials. Then we study the dimension of…

In this expository article we discuss the relations between Sasakian geometry, reduced holonomy and supersymmetry. It is well known that the Riemannian manifolds other than the round spheres that admit real Killing spinors are precisely…

Let V be a finite dimensional representation of the connected complex reductive group H. Denote by G the derived subgroup of H and assume that the categorical quotient of V by G is one dimensional. In this situation there exists a…

We prove a very general Kobayashi-Hitchin correspondence on arbitrary compact Hermitian manifolds. This correspondence refers to moduli spaces of "universal holomorphic oriented pairs". Most of the classical moduli problems in complex…

Let M be an almost complex manifold equipped with a Hermitian form such that its de Rham differential has Hodge type (3,0)+(0,3), for example a nearly Kahler manifold. We prove that any connected component of the moduli space of…

For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on…

Selective Rips complexes corresponding to a sequence of parameters are a generalization of Vietoris-Rips complexes utilizing the idea of thin simplices. We prove that if a metric space $Y$ is close (in Gromov-Hausdorff distance) to a closed…

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms,…

We study the holomorphic sections of the Deligne-Hitchin moduli space of a compact Riemann surface that are invariant under the natural anti-holomorphic involutions of the moduli space. Their relationships with the harmonic maps are…

In this paper we study weakly irreducible holonomy representations of the normal connection of a spacelike submanifold in a pseudo-Riemannian space from. We associate screen representations to weakly irreducible normal holonomy groups and…

We study the open/closed correspondence for the projective line via mirror symmetry. More explicitly, we establish a correspondence between the generating function of disk Gromov-Witten invariants of the complex projective line…

Let $X \subset \Bbb P^r$ be a smooth algebraic curve in projective space, over an algebraically closed field of characteristic zero. For each $m \in \Bbb N$, the $m$-flexes of $X$ are defined as the points where the osculating hypersurface…

We have studied irreducible real (respectively, quaternionic) Lie algebroid connections and prove that the Gauge theoretic moduli space has Hausdorff Hilbert manifold structure. This work generalises some known results about simple…

Let $M$ a compact connected orientable 4-manifold. We study the space $\Xi$ of $Spin^c$-structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on $M$. In order to study…

We give a sufficient condition for a meromorphic correspondence to be a holomorphic correspondence in a neighbourhood of a smooth real hypersurface

In this article, I define triangulated categories of constructible isocrystals on varieties over a perfect field of positive characteristic, in which Le Stum's abelian category of constructible isocrystals sits as the heart of a natural…