Related papers: On non-proper intersections and local intersection…
It is a well known that, for odd $n$, the number of subsets of $\{1,2,\dots,n\}$ the sum of whose elements is divisible by $n$ equals the number of binary necklaces of length $n$. In this paper generalize this result in two directions. On…
Generalized composite fluxbrane solutions for a wide class of intersection rules are obtained. The solutions are defined on a manifold which contains a product of n Ricci-flat spaces M_1 x ... x M_n with 1-dimensional M_1. They are defined…
We find general first-order equations for G_2 metrics of cohomogeneity one with S^3\times S^3 principal orbits. These reduce in two special cases to previously-known systems of first-order equations that describe regular asymptotically…
We study derived intersections of smooth analytic cycles, and provide in some cases necessary and sufficient conditions for this intersection be formal. In particular, if X is a complex submanifold of a complex manifold Y, we prove that X…
We show that if $M = X \times Y$ is the product of two complex manifolds (of positive dimensions), then $M$ does not admit any complete K\"ahler metric with bisectional curvature bounded between two negative constants. More generally, a…
Generalizing a formula of Stanley, we prove combinatorially that the probability that $1, 2, \dots, k$ are contained in the same cycle of a product of two random $n$-cycles is \[\frac{1}{k} + \frac{4 (-1)^n}{ \binom{2k}{k}}…
A digraph $D=(V(D)$, $A(D))$ of order $n\geq 3$ is pancyclic, whenever $D$ contains a directed cycle of length $k$ for each $k\in \{3,\ldots,n\}$; and $D$ is vertex-pancyclic iff, for each vertex $v\in V(D)$ and each $k\in \{3,\ldots,n\}$,…
For a family of polytopes of even dimension $2p$, known as \textit{dual-neighborly}, it has been shown for $p\ne 2$ that the associated intersection of quadrics is a connected sum of sphere products $S^p\times S^p$. In this article we give…
We introduce higher-dimensional module factorizations associated to a regular sequence. They include higher-dimensional matrix factorizations, which are commutative cubes consisting of free modules with edges being classical matrix…
Samuel conjectured in 1961 that a (Noetherian) local complete intersection ring that is a UFD in codimension at most three is itself a UFD. It is said that Grothendieck invented local cohomology to prove this fact. Following the philosophy…
We discuss some geometric problems related to the definitions of quasilocal mass proposed by Brown-York \cite{BYmass1} \cite{BYmass2} and Liu-Yau \cite{LY1} \cite{LY2}. Our discussion consists of three parts. In the first part, we propose a…
In this article we study the structure of residual intersections via constructing a finite complex which is acyclic under some sliding depth conditions on the cycles of the Koszul complex. This complex provides information on an ideal which…
We define the notion of mirror of a Calabi-Yau manifold with a stable bundle in the context of type II strings in terms of supersymmetric cycles on the mirror. This allows us to relate the variation of Hodge structure for cohomologies…
The product of smooth valuations on manifolds is described in terms of differential forms, Gelfand transforms and blow-up spaces. It is shown that the product extends partially to generalized valuations and corresponds geometrically to…
One of pressing problems in mathematical physics is to find a generalized Poincar\'e symmetry that could be applied to nonflat space-times. As a step in this direction we define the semidirect product of groupoids $\Gamma_0 \rtimes…
Within this research, two combinatorial bijections using Young diagrams were studied. The first is a special case of a bijective correspondence between two classes of combinatorial objects. Its proof, based on Young diagrams, establishes…
We consider probability measures on the real line or unit circle with Jacobi or Verblunsky coefficients satisfying an $\ell^p$ condition and a generalized bounded variation condition. This latter condition requires that a sequence can be…
We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds. We do not need to know the explicit formulas for the homoclinic orbits prior…
We show that essential punctured spheres in the complement of links with distance three bridge spheres have bounded complexity. We define the operation of tangle product, a generalization of both connected sum and Conway product. Finally,…
In this article, we investigate some properties of cyclic coverings of complex surfaces of general type branched along smooth curves that are numerically equivalent to a multiple of the canonical class. The main results concern coverings of…