Related papers: Maximal slope of tensor product of Hermitian vecto…

An orthogonal bundle over a curve has an isotropic Segre invariant determined by the maximal degree of a Lagrangian subbundle. This invariant, and the induced stratifications on moduli spaces of orthogonal bundles, were studied for bundles…

The paper deals with a complex polynomial $H$ in two variables having - a generic highest homogeneous part (without multiple zero lines), - nonconstant lower terms. In particular, under these conditions the polynomial $H$ has at least two…

Minkowski tensors, also known as tensor valuations, provide robust $n$-point information for a wide range of random spatial structures. Local estimators for point clouds, e.g., representing voxelized data, however, are unavoidably biased…

Let M be a compact Riemannian manifold without boundary and let E be a Riemannian vector bundle over M. If $\Sigma$ denotes the sphere subbundle of E, we look for embeddings of $\Sigma$ into E admitting a prescribed mean curvatures of…

In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…

In this paper, we address a question of Donaldson's on the best estimate that can be achieved for the transversality of an asymptotically holomorphic sequence of sections of increasing powers of a line bundle over an integral symplectic…

Kang et al. provided a path realization of the crystal graph of a highest weight module over a quantum affine algebra, as certain semi-infinite tensor products of a single perfect crystal. In this paper, this result is generalized to give a…

We prove that the maximal dimension of a Kummer space in the generic tensor product of $n$ cyclic algebras of degree 4 is $4 n+1$.

We study strongly graded vertex algebras and their strongly graded modules, which are conformal vertex algebras and their modules with a second, compatible grading by an abelian group satisfying certain grading restriction conditions. We…

Let $L$ be a (semi)-positive line bundle over a Kahler manifold, $X$, fibered over a complex manifold $Y$. Assuming the fibers are compact and non-singular we prove that the hermitian vector bundle $E$ over $Y$ whose fibers over points $y$…

In this paper, we prove effective upper bounds for effective sections of line bundles on projective varieties and hermitian line bundles on arithmetic varieties in terms of the volumes. They are effective versions of the Hilbert--Samuel…

In this article we study asymptotic slopes of strongly semistable vector bundles on a smooth projective surface. A connection between asymptotic slopes and strong restriction theorem of a strongly semistable vector bundle is shown. We also…

Let X be a projective geometrically irreducible non-singular algebraic curve defined over a finite field F of order $q^2$. If the number of F-rational points of X satisfies the Hasse-Weil upper bound, then X is said to be F-maximal. For a…

Let $T$ be a maximal torus of a semisimple complex algebraic group, $\mathrm{BS}(s)$ be the Bott-Samelson variety for a sequence of simple reflections $s$ and $\mathrm{BS}(s)^T$ be the set of $T$-fixed points of $\mathrm{BS}(s)$. We prove…

Let X be a smooth projective curve of genus g bigger then 2. For any vector bundle E on X let M_k(E) be the scheme of all rank k subbundles of E with maximal degree. For every integers r, k and x with 0<k<r, x positive and either x less…

In a previous paper, \cite{Berndtsson}, we have studied a property of subharmonic dependence on a parameter of Bergman kernels for a family of weighted $L^2$-spaces of holomorphic functions. Here we prove a result on the curvature of a…

The Hanson-Wright inequality is an upper bound for tails of real quadratic forms in independent subgaussian random variables. In this work, we extend the Hanson-Wright inequality for the maximum eigenvalue of the quadratic sum of random…

We obtain sharp bounds on the convergence rate of Markov chains on irreducible representations of finite general linear, unitary, and symplectic groups (in both odd and even characteristic) given by tensoring with Weil representations.

In this paper, we give some new characterizations of umbilic hypersurfaces in general warped product manifolds, which can be viewed as generalizations of the work in \cite{KLP18} and \cite{WX14}. Firstly, we prove the rigidity for…

Let $X$ be a smooth projective curve of genus $g$ over an algebraically closed field $k$ of characteristic $p>2$. We prove that any rank $3$ nilpotent semistable Higgs bundle $(E,\theta)$ on $X$ is a strongly semistable Higgs bundle. This…