Related papers: A survey on Seifert fiber space conjecture
The classical honeycomb conjecture asserts that any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal honeycomb tiling. Pappus discusses this problem in his preface to Book V. This paper…
The aim of this paper is to describe an approach to a a strengthened form of J. Tits' Centre Conjecture for spherical buildings. This is accomplished by generalizing a fundamental result of G. R. Kempf from Geometric Invariant Theory and…
Here we outline a proof for the 4-dimensional smooth Poincare Conjecture.
Around 1960, R. Palais and J. Cerf proved a fundamental result relating spaces of diffeomorphisms and imbeddings of manifolds: If V is a submanifold of M, then the map from Diff(M) to Imb(V,M) that takes f to its restriction to V is locally…
In this article, we investigate Serrano's conjecture for strictly nef divisors on projective bundles over higher dimensional smooth projective varieties.
Nous refutons, sous une certaine hypothese combinatoire, la "nonrevisiting path conjecture". Abstract: In this article, we give, under some hypothesis, a couterexample to the nonrevisiting path conjecture.
I present a brief survey of surveys, and their results and implications, intended to set the context for the ensuing discussion.
We provide new sufficient conditions under which Ryser's conjecture holds.
We study Mori fiber spaces over a two-dimensional base which satisfy the semistability assumption. As an application of our technique we give a new proof of the existence of semistable 3-fold flips.
We study geometrical aspects of the space of fibrations between two given manifolds M and B, from the point of view of Frechet geometry. As a first result, we show that any connected component of this space is the base space of a…
We study the existence problem and the enumeration problem for sections of Serre fibrations over compact orientable surfaces. When the fundamental group of the fiber is finite, a complete solution is given in terms of 2-dimensional…
The status and regime of validity of the famous Thorne hoop conjecture in spatially regular {\it charged} curved spacetimes are clarified.
One of the aims of this article is to provide a class of polynomial mappings for which the Jacobian conjecture is true. Also, we state and prove several global univalence theorems and present a couple of applications of them.
This paper is devoted to study the birational properties of the Albanese map. I generalize a theorem of Kawamata to tell when the Albanese map is surjective and when it is an algebraic fiber space.
We prove a conjecture due to Gica (Fibonacci Quarterly, 2008). Our proof is simple, uses only elementary abstract algebra, and generalizes to other recursive sequences.
Remarks on mathematical proof and the practice of mathematics.
The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…
We present a new proof of the Joints Theorem without taking derivatives. Then we generalize the proof to prove the Multijoints Conjecture and Carbery's generalization. All results are in any dimension over an arbitrary field.
Given a fibre space $X/S$ with the generic geometric fibre of Kodaira dimension $\geq 0$, we shall construct a variety $Y$ ramified over $X$ along such a horizontal hyperplane with respect to $X/S$ that Koll\'ar and Kawamata had proved…
A proof of Petri's general conjecture on the unobstructedness of linear systems on a general curve is proposed, using only the local properties of the deformation space of the pair (curve, line bundle).