相关论文: Threefold Thresholds

A classification theorem is given of projective threefolds that are covered by a two-dimensional family of lines, but not by a higher dimensional family.

We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based…

We study various topics, e.g. accumulation points by a mean, two types of derivative by a mean, two new continuity and a boundedness concepts, we construct new means from old ones, finally we investigate the limit of means.

We prove that every set of $n$ points in $\mathbb{R}^3$ spans $O(n^{295/197+\epsilon})$ unit distances. This is an improvement over the previous bound of $O(n^{3/2})$. A key ingredient in the proof is a new result for cutting circles in…

We show that terminal 3-fold divisorial contraction to a point of index $>1$ with non-minimal discrepancy may be factored into a sequence of flips, flops and divisorial contractions to a point with minimal discrepancies.

We provide conjectural necessary and (separately) sufficient conditions for the Hilbert scheme of points of a given length to have the maximum dimension tangent space at a point. The sufficient condition is claimed for 3D and reduces the…

Building on classical aspects of the theory of Diophantine approximation, we consider the collection of all accumulation points of normalized integer vector translates of points $q\alpha$ with $\alpha\in\mathbb{R}^d$ and $q\in\mathbb{Z}$.…

Accumulation point of period-tripling bifurcations for complexified Henon map is found. Universal scaling properties of parameter space and Fourier spectrum intrinsic to this critical point is demonstrated.

We present non-trivial examples of accumulation of secants for orbits (of real analytic three dimensional vector fields) having the origin as only $\omega$-limit point. These non-trivial sets have the structure of a proper algebraic variety…

We apply a conjectured inequality on third chern classes of stable two-term complexes on threefolds to Fujita's conjecture. More precisely, the inequality is shown to imply a Reider-type theorem in dimension three which in turn implies that…

We investigate the existence of complete intersection threefolds $X \subset \mathbb{P}^n$ with only isolated, ordinary multiple points and we provide some sufficient conditions for their factoriality.

We derive three-dimensional integrable mappings which have two invariants.

We give an example of a dynamical system which is mixing relative to one of its factors, but for which relative mixing of order three does not hold.

This is an example on the cohomology of threefolds.

We prove that subsets of ${\Bbb R}^d$, $d \ge 4$ of large enough Hausdorff dimensions contain vertices of an equilateral triangle. It is known that additional hypotheses are needed to assure the existence of equilateral triangles in two…

We review the state of the art of the classification of real uniruled threefolds

In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in…

We prove boundedness of rationally-connected threefolds in $\mathbb P^6$ under some extra-assumptions.

We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1.

We prove the existence of a geometric characteristic submanifold for non-positively curved manifolds of any dimension greater than or equal to three. In dimension three, our result is a geometric version of the topological characteristic…