On the genus of elliptic fibrations

A simply connected topological space is called elliptic if both and are finite-dimensional -vector spaces. In this paper, we consider fibrations for which the fibre is elliptic and is evenly graded. We show that in the generic cases, the genus of such a fibration is completely determined by generalized Chern classes of the fibration.

     

On base manifolds of Lagrangian fibrations

We consider base spaces of Lagrangian fibrations from singular symplectic varieties.After defining cohomologically irreducible symplectic varieties,we construct an example of Lagrangian fibration whose base space is isomorphic to a quotient of the projective space.We also prove that the base space of Lagrangian fibration from a cohomologically symplectic variety is isomorphic to the projective space provided that the base space is smooth.     

On almost holomorphic Lagrangian fibrations

We prove that the pull back of an ample line bundle by an almost holomorphic Lagrangian fibration is nef. As an application, we show birational semi rigidity of Lagrangian fibrations.     

On two results about fibrations

Using equivariant methods, we provide straightforward proofs of a result of Chachólski and a result of Spivak about fibrations.     

On canonical fibrations of algebraic surfaces

LetS be an algebraic surface of general type. If the canonical system |K _S | ofS is a pencil of genusg, we hope to find the largestc(g) such thatK _S ² ≥c(g)p _g +constant. We have known thatc(3)≤6. In this paper, we proved thatc(3)≥5.25.     

On the geometry of the space of smooth fibrations

We study geometrical aspects of the space of smooth fibrations between two given manifolds M and B, from the point of view of Fréchet geometry. As a first result, we show that any connected component of this space is the base space of a Fréchet-smooth principal bundle with the identity component of the group of diffeomorphisms of M as total space. Second, we prove that the space of fibrations is also itself the total space of a smooth Fréchet principal bundle with structure group the group of diffeomorphisms of the base B.     

On the Shafarevich conjecture for genus-2 fibrations

We prove a result about fundamental group of a smooth projective surface with ample canonical divisor which admits a genus two fibration. As a corollary we prove that the universal cover of such a surface is holomorphically convex. This proves the conjecture of Shafarevich for such surfaces. This article is dedicated to Madhav V. Nori.     

PL fibrations are fibrations in the PL category

Proper PL maps which are Hurewicz fibrations have the covering homotopy property in the PL category.     

On bifurcation braid monodromy of elliptic fibrations

We propose to study a new kind of monodromy homomorphism for families of regular elliptic fibrations of a given differentiable fibration type to get a hold on topological properties of moduli stacks of elliptic surfaces.In specific cases, including the most significant one, when all singular fibres are nodal irreducible rational curves, we compute the corresponding monodromy group, a subgroup of the mapping class group of the fibration base punctured at the singular values of the fibration.We study a tentative algebraic characterisation and give implications for the group of diffeomorphisms compatible with the fibration.     

On the moduli of surfaces admitting genus 2 fibrations

We investigate the structure of the components of the moduli space of surfaces of general type, which parametrize surfaces admitting nonsmooth genus 2 fibrations of nonalbanese type, over curves of genusg _b≥2.     

On exotic characteristic classes for spherical fibrations

We define for every so-called admissible relation r in the Steenrod algebra $\text{A}$ and for every oriented spherical fibration ξ over a CW-space an exotic characteristic class (mod 2) ε(r)(ξ), which is primitive and vanishes for sphere bundles. The set of exotic classes associated with the universal spherical fibration and the admissible Adem relations are compared with the algebra generators of H¹(BSG;$\text{Z}$₂) due to Milgram. Moreover, their behaviour under the action of $\text{A}$ is computed. Finally, we give a secondary Wu formula for exotic classes of special Poincaré duality spaces.     

On the fundamental group of hyperelliptic fibrations and some applications

We prove that for a hyperelliptic fibration on a surface of general type with irreducible fibers over a (possibly) non-complete curve, the image of the fundamental group of a general fiber in the fundamental group of the surface is finite. Examples show that the result is optimal. As a corollary of this result we prove two conjectures; the Shafarevich conjecture on holomorphic convexity for the universal cover of these surfaces, and a conjecture of Nori on the finiteness of the fundamental groups of some surfaces. We also prove a striking general result about the multiplicities of multiple fibers of a hyperelliptic fibration on a smooth, projective surface.     

On the existence of almost Fano threefolds with del Pezzo fibrations

By Jahnke–Peternell–Radloff and Takeuchi, almost Fano threefolds with del Pezzo fibrations were classified. Among them, there exist 10 classes such that the existence of members of these was not proved. In this paper, we construct such examples belonging to each of 10 classes.     

Mapping fibrations

We present a fibration theorem for mappings from C ⁿ to C ^p , withn <p that resembles the Milnor fibration theorem for isolated complete intersection singularities which is due to H. Hamm.