Related papers: On 4-dimensional smooth Poincare conjecture
In this article we show that every closed orientable smooth $4$--manifold admits a smooth embedding in the complex projective $3$--space.
We clarify the question whether for a smooth curve of polynomials one can choose the roots smoothly and related questions. Applications to perturbation theory of operators are given.
We prove a sharp square function estimate for the cone in $\mathbb{R}^3$ and consequently the local smoothing conjecture for the wave equation in $2+1$ dimensions.
Poincar\'e's Polyhedron Theorem is a widely known valuable tool in constructing manifolds endowed with a prescribed geometric structure. It is one of the few criteria providing discreteness of groups of isometries. This work contains a…
A strong form of the Manin-Peyre conjecture with a power saving error term is proved for a certain cubic fourfold.
We give a relatively short and elementary proof of Manin's conjecture for split smooth quintic del Pezzo surfaces over the rational numbers.
Given a curve over a finite field, we compute the number of stable bundles of not necessarily coprime rank and degree over it. We apply this result to compute the virtual Poincare polynomials of the moduli spaces of stable bundles over a…
We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof…
In this paper, we prove that the statement: ``The (Generalized) Hodge Conjecture holds for codimension-two cycles on a smooth projective variety $X$" is a birationally invariant statement, that is, if the statement is true for $X$, it is…
We provide a new proof for maximal monotonicity of the subdifferential of a convex function.
We prove the thin set version of Manin's conjecture for the chordal (or: determinantal) cubic fourfold, which is the secant variety of the Veronese surface. We reduce this counting problem to a result of Schmidt for quadratic points in the…
Assuming the Riemann hypothesis we demonstrate the existence of smooth numbers in certain short intervals.
We prove the volume conjecture for any twist knots by using an equivalence relation, complex analysis, analytic continuation, and function of several complex variables on the basis of colored Jones polynomials.
We present test results for the smooth lattice method using an Oppenheimer-Snyder spacetime. The results are in excellent agreement with theory and numerical results from other authors.
In this paper we address the relation between the orbifold fundamental group and the topology of the underlying space. In particular, under the assumption that the orbifold fundamental group is equal to the fundamental group of the…
Let $Y$ be a geometrically irreducible reduced projective curve defined over real numbers. Let $U_Y$ (respectively, $U'_Y$) be the moduli space of geometrically stable torsionfree sheaves (respectively, locally free sheaves) on $Y$ of rank…
We prove that any smooth cubic surface defined over any number field satisfies the lower bound predicted by Manin's conjecture possibly after an extension of small degree.
The Manin conjecture is established for a split singular del Pezzo surface of degree four, with singularity type A_4.
A proof of Sendov's conjecture is given.
The classical Poincar{\'e} conjecture that every homotopy 3-sphere is diffeomorphic to the 3-sphere is confirmed by Perelman in arXiv papers solving Thurston's program on geometrizations of 3-manifolds. A new confirmation of this conjecture…