Related papers: Incidence Divisor

We prove that every mod 2 integral cycle $T$ in a Riemannian manifold $\mathcal{M}$ can be approximated in flat norm by a cycle which is a smooth submanifold $\Sigma$ of nearly the same area, up to a singular set of codimension 3; in…

For a bipartite graph $H$, its linear threshold is the smallest real number $\sigma$ such that every bipartite graph $G = (U \sqcup V, E)$ with unbalanced parts $|V| \gtrsim |U|^\sigma$ and without a copy of $H$ must have a linear number of…

Let $R$ be a commutative ring with non-zero identity. We describe all $C_3$- and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. Also, we shall describe all…

Let $p$ be a prime number, and let $\Delta_1,\Delta_2 < 0$ be two coprime fundamental discriminants. When $p$ splits in $\mathbb{Q}(\sqrt{\Delta_1})$ and $\mathbb{Q}(\sqrt{\Delta_2})$ the height pairings of the corresponding CM divisors on…

For a monotone symplectic manifold and a smooth anticanonical divisor, there is a formal deformation of the symplectic cohomology of the divisor complement, defined by allowing Floer cylinders to intersect the divisor. We compute this…

We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…

Let $X$ be a contractible $2$-complex which is a union of two contractible subcomplexes $Y$ and $Z.$ Is the intersection $Y\cap Z$ contractible as well? In this note, we prove that the inclusion-induced map $\pi _{1}(Y\cap Z)\rightarrow \pi…

This paper presents a proof of the existence of standard symplectic coordinates near a set of smooth, orthogonally intersecting symplectic submanifolds. It is a generalization of the standard symplectic neighborhood theorem. Moreover, in…

We extend Reider's freeness criterion to normal surfaces of characteristic 0. Let Y be a normal surface. Let D be a nef divisor on Y such that K_Y+D is a Cartier divisor. Let x be a point on Y. If x is a base point of |K_Y+D| and…

A graph $G$ realizes the degree sequence $S$ if the degrees of its vertices is $S$. Hakimi gave a necessary and sufficient condition to guarantee that there exists a connected multigraph realizing $S$. Taylor later proved that any connected…

The universal Vassiliev-Kontsevich invariant is a functor from the category of tangles to a certain graded category of chord diagrams, compatible with the Vassiliev filtration and whose associated graded is an isomorphism. The Vassiliev…

Given a compact orientable surface $\Sigma$, let $\Cal S(\Sigma)$ be the set of isotopy classes of essential simple loops on $\Sigma$. We determine a complete set of relations for a function from $\Cal S(\Sigma)$ to $\bold Z$ to be a…

The cycle double cover conjecture states that a graph is bridge-free if and only if there is a family of edge-simple cycles such that each edge is contained in exactly two of them. It was formulated independently by Szekeres (1973) and…

The objective of this article is to give an effective algebraic characterization of normal crossing hypersurfaces in complex manifolds. It is shown that a hypersurface has normal crossings if and only if it is a free divisor, has a radical…

Let $F(x)$ be an irreducible polynomial with integer coefficients and degree at least 2. For $x\ge z\ge y\ge 2$, denote by $H_F(x, y, z)$ the number of integers $n\le x$ such that $F(n)$ has at least one divisor $d$ with $y<d\le z$. We…

We show that the image of a dominant meromorphic map from an irreducible compact Calabi-Yau manifold $X$ whose general fiber is of dimension strictly between $0$ and $\dim X$ is rationally connected. Using this result, we construct for any…

We prove the following theorem. Let $r\ge 4$ be an integer, and $G$ be a $K_{1,r}$-free $r$-edge-connected $r$-regular graph. Then, for every set $W$ of even number of vertices of $G$ such that the distance between any two vertices of $W$…

We establish a close connection between the intersection multiplicity of three arithmetic Hirzebruch-Zagier cycles and the Fourier coefficients of the derivative of a certain Siegel-Eisenstein series at its center of symmetry. Our main…

Hilbert famously showed that polynomials in n variables are not too complicated, in various senses. For example, the Hilbert Syzygy Theorem shows that the process of resolving a module by free modules terminates in finitely many (in fact,…

In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain diverse tangency points. We show that the slow divergence…