Related papers: Logarithmic Cartan geometry on complex manifolds

In this paper, we provide an upgrade of Deligne's geometric class field theory for tamely ramified Galois groups using logarithmic geometry. In particular, we define a framed logarithmic Picard space, and show that a logarithmic…

This is a survey paper dealing with holomorphic G-structures and holomorphic Cartan geometries on compact complex manifolds. Our emphasis is on the foliated case: holomorphic foliations with transverse (branched or generalized) holomorphic…

We study local automorphisms of holomorphic Cartan geometries. This leads to classification results for compact complex manifolds admitting Cartan geometries. We prove that a compact Calabi-Yau manifold bearing a holomorphic Cartan geometry…

We prove that if a Calabi--Yau manifold $M$ admits a holomorphic Cartan geometry, then $M$ is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on compact K\"ahler manifolds. We also…

We classify holomorphic Cartan geometries on every compact complex curve, and on every compact complex surface which contains a rational curve.

In this paper, we investigate the possibility of constructing isomonodromic deformations of logarithmic connections on curves by using ramified covers. We give new examples and prove a classification result.

We extend the notion of (branched) holomorphic Cartan geometry on a complex manifold to the context of Sasakian manifolds. Branched holomorphic Cartan geometries on Sasakian Calabi-Yau manifolds are investigated.

Earlier we introduced and studied the concept of holomorphic {\it branched Cartan geometry}. We define here a foliated version of this notion; this is done in terms of Atiyah bundle. We show that any complex compact manifold of algebraic…

In this paper we show that Cartan geometries can be studied via transitive Lie groupoids endowed with a special kind of vector-valued multiplicative 1-forms. This viewpoint leads us to a more general notion, that of Cartan bundle, which…

A typical example of a Cartan calculus consists of the Lie derivative and the contraction with vector fields of a manifold on the derivation ring of the de Rham complex. In this manuscript, a second stage of the Cartan calculus is…

This is largely a survey paper, dealing with Cartan geometries in the complex analytic category. We first remind some standard facts going back to the seminal works of F. Klein, E. Cartan and C. Ehresmann. Then we present the concept of a…

We introduce the notion of Galois holomorphic foliation on the complex projective space as that of foliations whose Gauss map is a Galois covering when restricted to an appropriate Zariski open subset. First, we establish general criteria…

Let $X$ be a compact Riemann surface, $\Sigma$ a finite set of points and $M = X\setminus \Sigma$. We study the $L^2$ cohomology of a polarized complex variation of Hodge structure on a Galois covering of the Riemann surface of finite type…

We show that compact complex manifolds of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the…

We make a case for the unique relevance of Cartan geometry for gauge theories of gravity and supergravity. We introduce our discussion by recapitulating historical threads, providing motivations. In a first part we review the geometry of…

Let $M$ be a compact complex manifold, and $D\, \subset\, M$ a reduced normal crossing divisor on it, such that the logarithmic tangent bundle $TM(-\log D)$ is holomorphically trivial. Let ${\mathbb A}$ denote the maximal connected subgroup…

We construct a logarithmic version of the Hilbert scheme, and more generally the Quot scheme, of a simple normal crossings pair. The logarithmic Quot space admits a natural tropicalisation called the space of tropical supports, which is a…

We introduce linear Dirac and generalized complex structures on Cartan geometries and give criteria for Dirac subalgebras of $\frkg\ltimes\frkg^*$ representing Dirac structures on a Cartan geometry. We prove that there is a bijection…

A linear connection on a Lie algebroid is called a Cartan connection if it is suitably compatible with the Lie algebroid structure. Here we show that a smooth connected manifold $M$ is locally homogeneous - i.e., admits an atlas of charts…

In this paper we give a unified approach in categorical setting to the problem of finding the Galois closure of a finite cover, which includes as special cases the familiar finite separable field extensions, finite unramified covers of a…