Related papers: Complex Hyperbolic Structures on Disc Bundles over…

Extending a result of Morita, we show that all tautological classes of the moduli space of genus g curves are bounded. As an application, we obtain that for a surface bundle $E\to B$ over a closed surface, the Eulder characteristic…

The Hodge Conjecture is equivalent to a statement about conditions under which a complex vector bundle on a smooth complex projective variety admits a holomorphic structure. I advertise a class of abelian four-folds due to Mumford where…

We consider topologically non-trivial Higgs bundles over elliptic curves with marked points and construct corresponding integrable systems. In the case of one marked point we call them the modified Calogero-Moser systems (MCM systems).…

An SU(3)- or SU(1,2)-structure on a 6-dimensional manifold N^6 can be defined as a pair of a 2-form omega and a 3-form rho. We prove that any analytic SU(3)- or SU(1,2)-structure on N^6 with d omega^2 =0 can be extended to a parallel…

We show that a compact Kahler manifold admitting a nondegenerate holomorphic 2-form valued in a line bundle is a finite cyclic cover of a hyperkahler manifold. With respect to the connection induced by the locally hyperkahler metric, the…

We explore algebro-geometric properties of the moduli space of holomorphic Lie algebroid ($ \mathcal{L} $) connections on a compact Riemann surface $X$ of genus $g \,\geq\, 3$. A smooth compactification of the moduli space of…

In this paper we define and study pseudoholomorphic vector bundles structures, particular cases of which are tangent and normal bundle almost complex structures. These are intrinsically related to the Gromov D-operator. As an application we…

Let $\bar{L}_i\lr X_i$ be a holomorphic line bundle over a compact complex manifold for $i=1,2$. Let $S_i$ denote the associated principal circle-bundle with respect to some hermitian inner product on $\bar{L}_i$. We construct complex…

Let $ \mathcal{D} = \{D_{1}, ..., D_{\ell}\} $ be a multi-degree arrangement with normal crossings on the complex projective space $ \mathbf{P}^{n} $, with degrees $ d_{1}, ..., d_{\ell} $; let $ \Omega_{\mathbf{P}^{n}}^{1}(\log…

A holomorphic triple over a compact Riemann surface consists of two holomorphic vector bundles and a holomorphic map between them. After fixing the topological types of the bundles and a real parameter, there exist moduli spaces of stable…

We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This extends some aspects of the combinatorial model for doubly…

We study holomorphic $(n+1)$-chains $E_n\to E_{n-1} \to >... \to E_0$ consisting of holomorphic vector bundles over a compact Riemann surface and homomorphisms between them. A notion of stability depending on $n$ real parameters was…

Since the set of volumes of hyperbolic 3-manifolds is well ordered, for each fixed g there is a genus-g surface bundle over the circle of minimal volume. Here, we introduce an explicit family of genus-g bundles which we conjecture are the…

In this article we show that for every collection $\mathcal{C}$ of an even number of polynomials, all of the same degree $d>2$ and in general position, there exist two hyperbolic $3$-orbifolds $M_1$ and $M_2$ with a M\"obius morphism…

We construct explicit geometric models for moduli spaces of semi-stable strongly parabolic Higgs bundles over the Riemann sphere, in the case of rank two, four marked points, arbitrary degree, and arbitrary weights. The mechanism of…

We give a complete description of the two-dimensional moduli spaces of stable Higgs bundles of rank 2 over complex projective line with one irregular singular point, having a regular leading-order term, and endowed with a generic compatible…

This paper deals with a limiting case motivated by contact geometry. The limiting case of a tensorial characterization of contact hypersurfaces in Kahler manifolds leads to Hopf hypersurfaces whose maximal complex subbundle of the tangent…

Since the sixties it is well known that there are no non-trivial closed holomorphic $1$-forms on the moduli space $\mathcal{M}_g$ of smooth projective curves of genus $g>2$. In this paper, we strengthen such result proving that for $g\geq…

We extend Atiyah's holomorphic jet bundle formalism to holomorphic vector bundles over noncommutative algebras endowed with a bigraded differential calculus truncated at bidegree $(1,1)$; we refer to such structures as noncommutative…

Using global considerations, Mess proved that the moduli space of globally hyperbolic flat Lorentzian structures on $S\times\mathbb{R}$ is the tangent bundle of the Teichm\"uller space of $S$, if $S$ is a closed surface. One of the goals of…