Related papers: Condition of intersecting a projective variety wit…

Given a compact Lagrangian $L$ in a semipositive convex-at-infinity symplectic manifold $W$, we establish a cup-length estimate for the action values of $L$ associated to a Hamiltonian isotopy whose spectral norm is smaller than some…

Given a graph, an $L(p,1)$-labeling of the graph is an assignment $f$ from the vertex set to the set of nonnegative integers such that for any pair of vertices $(u,v),|f (u) - f (v)| \ge p$ if $u$ and $v$ are adjacent, and $f(u) \neq f(v)$…

We consider the mixed problem for $L$ the Lam\'e system of elasticity in a bounded Lipschitz domain $ \Omega\subset\reals ^2$. We suppose that the boundary is written as the union of two disjoint sets, $\partial\Omega =D\cup N$. We take…

We discuss the property of (almost) complete intersection of LSS-ideals of graphs of some special forms, like trees, unicyclic, and bicyclic graphs. Further, we give a sufficient condition for the complete intersection property of twisted…

Let $P_{\lambda\Sigma_n}$ be the Ehrhart polynomial associated to an intergal multiple $\lambda$ of the standard symplex $\Sigma_n \subset \mathbb{R}^n$. In this paper we prove that if $(M, L)$ is an $n$-dimensional polarized toric manifold…

Let $X$ be a smooth projective surface over the complex number field and let $L$ be a nef-big divisor on $X$. Here we consider the following conjecture; If the Kodaira dimension $\kappa(X)\geq 0$, then $K_{X}L\geq 2q(X)-4$, where $q(X)$ is…

Consider a uniformly distributed random linear subspace $L$ and a stochastically independent random affine subspace $E$ in $\mathbb{R}^n$, both of fixed dimension. For a natural class of distributions for $E$ we show that the intersection…

We define and study a notion of minimal exponent for a locally complete intersection subscheme $Z$ of a smooth complex algebraic variety $X$, extending the invariant defined by Saito in the case of hypersurfaces. Our definition is in terms…

Let $X$ be a compact normal complex space of dimension $n$ and $L$ be a holomorphic line bundle on $X$. Suppose that $\Sigma=(\Sigma_1,\ldots,\Sigma_\ell)$ is an $\ell$-tuple of distinct irreducible proper analytic subsets of $X$,…

Intersecting codes are a classical object in coding theory whose rank-metric analogue has recently been introduced. Although the definition formally parallels the Hamming-metric case, the structure and parameter constraints of rank-metric…

For Banach spaces $X,Y,$ we consider a distance problem in the space of bounded linear operators $\mathcal{L}(X,Y).$ Motivated by a recent paper \cite{RAO21}, we obtain sufficient conditions so that for a compact operator…

Given a real projective variety $X$ and $m$ ample line bundles $L_1,\dots L_m$ on $X$ also defined over $\mathbb{R}$, we study the topology of the real locus of the complete intersections defined by global sections of $L_1^{\otimes…

In this paper we establish an improved bound for the number of incidences between a set $P$ of $m$ points and a set $H$ of $n$ planes in $\mathbb R^3$, provided that the points lie on a two-dimensional nonlinear irreducible algebraic…

We consider the mirrors model in $d$ dimensions on an infinite slab and with unit density. This is a deterministic dynamics in a random environment. We argue that the crossing probability of the slab goes like $\kappa/(\kappa+N)$ where $N$…

In $PG(3,q^2)$, with $q$ odd, we determine the possible intersection sizes of a Hermitian surface $\mathcal{H}$ and an irreducible quadric $\mathcal{Q}$ having the same tangent plane $\pi$ at a common point $P\in{\mathcal Q}\cap{\mathcal…

Suppose we have $r$ hypersurfaces in $\mathbb{P}^m$ of degree $d$, whose defining polynomials are linearly independent, and their intersection has dimension $0$. Then what is the largest possible intersection of the $r$ hypersurfaces? We…

We define a new family of open Gromov-Witten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold…

We consider relative character varieties on $\mathbb{P}^1\backslash\{0,1,\infty\}$ with $G=GL(r), O(r)$, or $Sp(r)$. Using a diagrammatic method of Simpson's, we give an explicit linear upper bound $R(d)$ on the rank $r$ of an MC-minimal…

Understanding the statistics of collisions among locally confined gas particles poses a major challenge. In this work we investigate $\mathbb Z^d$-map lattices coupled by collision with simplified local dynamics that offer significant…

Let X be a complex analytic manifold. Given a closed subspace $Y\subset X$ of pure codimension p>0, we consider the sheaf of local algebraic cohomology $H^p_{[Y]}({\cal O}_X)$, and ${\cal L}(Y,X)\subset H^p_{[Y]}({\cal O}_X)$ the…