Related papers: Seshadri constants on Bott towers

In this paper, using Klyachko's classification theorem we study positivity and semi-stability of toric vector bundles on a class of nonsingular projective toric varieties, known as Bott towers. In particular, we give a criterion of $s$-jet…

A comparison problem for volumes of convex bodies asks whether inequalities $f_K(\xi)\le f_L(\xi)$ for all $\xi\in S^{n-1}$ imply that $\vol_n(K)\le \vol_n(L),$ where $K,L$ are convex bodies in $\R^n,$ and $f_K$ is a certain geometric…

A standard monomial theory for Schubert varieties is constructed exploiting (1) the geometry of the Seshadri stratifications of Schubert varieties by their Schubert subvarieties and (2) the combinatorial LS-path character formula for…

We develop strong lower bounds for the span of the projective Stiefel manifolds $X_{n,r}=O(n)/(O(n-r)\times \mathbb Z/2)$, which enable very accurate (in many cases exact) estimates of the span. The technique, for the most part, involves…

In this note, we study Seshadri constants and Gromov widths of toric surfaces via lattice widths of their moment polygons. We give the sharp lower bound of the ratio between the Gromov width of a symplectic toric $4$-fold and the lattice…

We prove that given any set of $n$ unit vectors $\{v_i\}_{i=1}^{n}\subset \mathbb R^n,$ the inequality \[ \sup\limits_{\Vert x \Vert_{\mathbb R^n} =1} \vert \langle x, v_1 \rangle \cdots \langle x, v_n\rangle\vert \ge n^{-n/2} \] holds for…

We investigate the standard stable manifold theorem in the context of a partially hyperbolic singu-larity of a vector field depending on a parameter. We prove some estimates on the size of the neighbourhood where the local stable manifold…

We construct vector bundles $R^r_\mu$ on a smooth projective curve $X$ having the property that for all sheaves $E$ of slope $\mu$ and rank $r$ on $X$ we have an equivalence: $E$ is a semistable vector bundle $\iff$ $Hom(R^r_\mu,E)=0$. As a…

Let $H(\epsilon, x)$ be a finite dimensional hermitian matrix depending on the variable $x$ taking its values on a 2D manifold and changing with $\epsilon$. If at $\epsilon=0$ two bands are touching, we give a formula for the change of…

We introduce a non-perturbative framework for computing structure constants of single-trace operators in the N=4 SYM theory at large N. Our approach features new vertices, with hexagonal shape, that can be patched together into three- and…

Given an additively written abelian group $G$ and a set $X\subseteq G$, we let $\mathscr{B}(X)$ denote the monoid of zero-sum sequences over $X$ and $\mathsf{D}(X)$ the Davenport constant of $\mathscr{B}(X)$, namely the supremum of the…

We provide an upper bound for the Gromov width of compact homogeneous Hodge manifolds $(M, \omega)$ with $b_2(M)=1$. As an application we obtain an upper bound on the Seshadri constant $\epsilon (L)$ where $L$ is the ample line bundle on…

Let $X_1,\ldots,X_N$, $N>n$, be independent random points in $\mathbb{R}^n$, distributed according to the so-called beta or beta-prime distribution, respectively. We establish threshold phenomena for the volume, intrinsic volumes, or more…

We report on non-perturbative bounds for structure constants on N=4 SYM. Such bounds are obtained by applying the conformal bootstrap recently extended to superconformal theories. We compare our results with interpolating functions suitably…

Let X be an irreducible smooth projective curve defined over complex numbers, S= {p_1, p_2,...,p_n} \subset X$ a finite set of closed points and N > 1 a fixed integer. For any pair (r,d) in Z X Z/N, there exists a parabolic vector bundle…

The isotropy constant of any $d$-dimensional polytope with $n$ vertices is bounded by $C \sqrt{n/d}$ where $C>0$ is a numerical constant.

We study the Waldschmidt constant of some configurations in the projective plane. In the first part, we show that the Waldschmidt constant of a set $\mathbb{X}$ of $n$ points where at least $n-3$ points among them lie on a line is either…

In this notes we study $k$-jet ample line bundles $L$ on a non singular toric variety $X$, i.e. line bundles with global sections having arbitrarily prescribed $k$-jets at a finite number of points. We introduce the notion of an associated…

We study the following question: Given a vector bundle on a projective variety $X$ such that the restriction of $E$ to every closed curve $C \,\subset\, X$ is ample, under what conditions $E$ is ample? We first consider the case of an…

The main goal of this paper is to present a new algorithm bounding the regularity and ``alpha'' (the lowest degree of existing hypersurface) of a linear system of hypersurfaces (in $\mathbb P^n$) passing through multiple points in general…