Fano manifolds with Lefschetz defect 3

Noncomplex Smooth 4-manifolds with Lefschetz Fibrations

Recently, B. Ozbagci and A. Stipsicz [12] proved that there are infinitely many pairwise nonhomeomorphic 4-manifolds admitting genus-2 Lefschetz fibration over S but not carrying any complex structure with either orientation. (For the definition of Lefschetz fibration, see [6].) Their result depends on a relation in the mapping class group of a closed orientable surface of genus 2. This relatio...

Mirror Symmetry and Fano Manifolds

Lefschetz Fibrations of 4-Dimensional Manifolds

An n-dimensional manifold is an object which locally resembles n-dimensional Euclidean space. Different categories of manifolds can be considered simply by requiring different sorts of maps to perform these local identifications: A manifold may be smooth (if the maps are required to be infinitely differentiable), or complex (if n is even and the maps are required to be holomorphic), or topologi...

Lefschetz Type Pencils on Contact Manifolds

We define the concept of Lefschetz contact pencil and we show the existence of such structures on any contact manifold. The main idea of the proof is a generalization of the Donaldson arguments used in the symplectic case. We will analyze some of the applications of such existence theorem for the topology of approximately holomorphic contact submanifolds. In particular, we study the topological...

Lefschetz Fibrations on Compact Stein Manifolds

Here we prove that up to diffeomorphism every compact Stein manifold W of dimension 2n + 2 > 4 admits a Lefschetz fibration over the disk D with Stein regular fibers, such that the monodromy of the fibration is a symplectomorphism induced by compositions of right-handed Dehn twists along embedded Lagrangian n-spheres on the generic fiber. This generalizes the Stein surface case of n = 1, previo...