Related papers: A survey on Seifert fiber space conjecture

We give a conceptual explanation for the somewhat mysterious origin of Suslin matrices. This enables us to generalize the construction of Suslin matrices and to give more conceptual proofs of some well-known results.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

We revise a proof of a Mazur-Ulam theorem for generalized gyrovector spaces.

Using deformation theory of rational curves, we prove a conjecture of Sommese on the extendability of morphisms from ample subvarieties when the morphism is a smooth (or mildly singular) fibration with rationally connected fibers. We apply…

We describe the behaviour of the rank of the Mordell-Weil group of the Picard variety of the generic fibre of a fibration in terms of local contributions given by averaging traces of Frobenius acting on the fibres. The results give a…

Let $M$ be a closed symplectic manifold and suppose $M\to P\to B$ is a Hamiltonian fibration. Lalonde and McDuff raised the question whether one always has $H^*(P;\mathbb Q)=H^*(M;\mathbb Q)\otimes H^*(B;\mathbb Q)$ as vector spaces. This…

Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.

Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler conjecture {\mf for symmetric convex bodies}. Our contributions include, in particular, simple self-contained proofs of their two key statements.…

We give a proof of some small weight and level cases of Serre's conjecture.

Recently Stephen Theriault and I found an elementary construction of Anick's spaces and proved their main properties(arXiv:0710.1024).In this work the fundamental fibration is decomposed. This is useful in studying maps out of Anick's…

In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.

We give a slope equality for fibered surfaces whose general fiber is a smooth plane curve. As a corollary, we prove a "strong" Durfee-type inequality for isolated hypersurface surface singularities, which implies Durfee's strong conjecture…

In this paper we present the statement of the Firoozbakht's conjecture, some of its consequences if it is proved and we show a consequence of Zhang's theorem concerning the Firoozbakht's conjecture.

We investigate Beauville's conjecture on the Chow ring of irreducible symplectic varieties. For special irreducible symplectic varieties we relate it to a conjecture on the existence of rational Lagrangian fibrations, which proves…

We present some motivations and discuss various aspects of an approach to the Jacobian Conjecture in terms of irreducible elements and square-free elements.

Starting with an Abelian fiber space, the aim is to construct a Tate-Shafarevich twist that has a rational section.

We relate the Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces to the existence of Shokurov polytopes. For K3 fibrations, the existence of (weak) fundamental domains for movable cones is established. The relationship between…

A detailed analysis of the PPT square conjecture is given.

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.