Related papers: Some examples due to H. Hironaka

We construct some families of complex structures on compact manifolds by means of normal almost contact structures (nacs) so that each complex manifold in the family has a non-singular holomorphic flow. These families include as particular…

We present a simplified proof for a recent theorem by Junyan Cao and Mihai Paun, confirming a special case of Iitaka's conjecture: if $f \colon X\to Y$ is an algebraic fiber space, and if the Albanese mapping of $Y$ is generically finite…

We give new homotopy theoretic criteria for deciding when a fibration with homotopy finite fibers admits a reduction to a fiber bundle with compact topological manifold fibers. The criteria lead to a new and unexpected result about…

Let X be a projective surface, let \sigma be an automorphism of X, and let L be a \sigma-ample invertible sheaf on X. We study the properties of a family of subrings, parameterized by geometric data, of the twisted homogeneous coordinate…

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…

This survey paper is devoted to Riemannian manifolds with special holonomy. To any Riemannian manifold of dimension n is associated a closed subgroup of SO(n), the holonomy group; this is one of the most basic invariants of the metric. A…

An example of a finite dimensional factorizable ribbon Hopf C-algebra is given by a quotient H=u_q(g) of the quantized universal enveloping algebra U_q(g) at a root of unity q of odd degree. The mapping class group M_{g,1} of a surface of…

We show that in every dimension greater than or equal to 4, there exist compact Kaehler manifolds which do not have the homotopy type of projective complex manifolds. Thus they a fortiori are not deformation equivalent to a projective…

We prove a new patchworking theorem for singular algebraic curves, which states the following. Given a complex toric threefold $Y$ which fibers over ${\mathbb C}$ with a reduced reducible zero fiber $Y_0$ and other fibers $Y_t$ smooth, and…

Motivated by index theory for semisimple groups, we study the relationship between the foliation C^*-algebras on manifolds admitting multiple fibrations. Let F_1,...,F_r be a collection of smooth foliations of a manifold X. We impose a…

We give a representation of the extension class associated to a holomorphic fibration by curvature, generalizing the work of Atiyah on holomorphic principal bundles in a natural way. As an application, we obtain a nonlinear analogue of the…

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is…

Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebra A with a fixed projection p. The resulting space P(p) admits a rich geometrical structure as a…

Given a fixed product of non-isogenous abelian varieties at least one of which is general, we show how to construct complete families of indecomposable abelian varieties whose very general fiber is isogenous to the given product and whose…

Hiss and Szczepa\'nski proved in 1991 that the holonomy group of any compact flat Riemannian manifold, of dimension at least two, acts reducibly on the rational span of the Euclidean lattice associated with the manifold via the first…

In very rough terms, the main theorem is that the set, which consists of semistable vector bundles with trivial rational Chern classes and nontrivial kth cohomology on a smooth complex projective variety, is a degeneration of a union of…

This article is concerned with a geometric tool given by a pair of projector operators defined by almost product structures on finite dimensional manifolds, polarized by a distribution of constant rank and also endowed with some geometric…

This note is devoted to the study of the homology class of a compact Poisson transversal in a Poisson manifold. For specific classes of Poisson structures, such as unimodular Poisson structures and Poisson manifolds with closed leaves, we…

We say that the the germ of a singular holomorphic foliation on $(\mathbb{C}^2,0)$ is algebraizable whenever it is holomorphically conjugate to the singularity of a foliation defined globally on a projective algebraic surface. The object of…

We give a classification of many closed Riemannian manifolds M whose universal cover possesses a nontrivial amount of symmetry. More precisely, we consider closed Riemannian manifolds $M$ such that Isom$(\widetilde{M})$ has noncompact…