Related papers: Skew-symmetric matrices and Palatini scrolls

Using properties of skew-Hamiltonian matrices and classic connectedness results, we prove that the moduli space $M_{ort}^0(r,n)$ of stable rank $r$ orthogonal vector bundles on $\mathbb{P}^2$, with Chern classes $(c_1,c_2)=(0,n)$, and…

Let $X = \bigcup_k X_k$ be the ind-Grassmannian of codimension $n$ subspaces of an infinite-dimensional torus representation. If $\cE$ is a bundle on $X$, we expect that $\sum_j (-1)^j \Lambda^j(\cE)$ represents the $K$-theoretic…

For an irreducible projective variety X, we study the family of h-planes contained in the secant variety Sec_k(X), for 0<h<k. These families have an expected dimension and we study varieties for which the expected dimension is not attained;…

Let $\sigma$ be a simple involution of an algebraic semisimple group $G$ and let $H$ be the subgroup of $G$ of points fixed by $\sigma$. If the restricted root system is of type $A$, $C$ or $BC$ and $G$ is simply connected or if the…

This article examines the structure of plane wave spacetimes (of signature $(1,n+1)$, $n\ge 2$) that are homogeneous (the isometry group is transitive) and geodesically complete -- which we call microcosms. In general, a plane wave is shown…

In this paper we study equivariant moduli spaces of sheaves on a $ K3 $ surface $ X $ under a symplectic action of a finite group. We prove that under some mild conditions, equivariant moduli spaces of sheaves on $ X $ are irreducible…

Let X be a symplectic or odd orthogonal Grassmannian parametrizing isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in…

Let $(M, g)$ be a compact 3-manifold with nonnegative scalar curvature $R_g\geq 0$. The boundary $\partial M$ is diffeomorphic to the boundary of a rotationally symmetric and weakly convex body $\bar{M}$ in $\mathbb{R}^3$. We call…

From the viewpoint of mirror symmetry, we revisit the hypergeometric system $E(3,6)$ for a family of K3 surfaces. We construct a good resolution of the Baily-Borel-Satake compactification of its parameter space, which admits special…

We study linear projections on Pluecker space whose restriction to the Grassmannian is a non-trivial branched cover. When an automorphism of the Grassmannian preserves the fibers, we show that the Grassmannian is necessarily of…

Suppose that a Hilbert scheme of points on a K3 surface S of Picard rank one admits a rational Lagrangian fibration. We show that if the degree of the surface is sufficiently large compared to the number of points, then the Hilbert scheme…

In the recent paper [arXiv:1612.06893] P. B\"urgisser and A. Lerario introduced a geometric framework for a probabilistic study of real Schubert Problems. They denoted by $\delta_{k,n}$ the average number of projective $k$-planes in…

We consider graded Cartan matrices of the symmetric groups and the Iwahori-Hecke algebras of type A, which have entries in the ring $\mathbb Z[v,v^{-1}]$. These matrices may also be interpreted as Gram matrices of the Shapovalov form on…

Let $C$ be a smooth projective irreducible curve of genus $g$. And let $G_{\alpha}(n,d,l)$ be the moduli space of $\alpha$ stable pairs of a vector bundle of $\rank n, \deg d$ and a subspace of $H^0(C,E)$ of $\dim = l $. We find an explicit…

We investigate pairwise quasi-orthogonal subalgebras in $M_{p^{kn}}$ which are isomorphic to $M_{p^{k}}$ for $k \ge 1$, $n \ge 2$ and a prime number $p$ with $p \ge 3$. We prove there exist $p^{2kn}-1/p^{2k}-1$ such subalgebras and they…

In this paper we prove a conjecture on the dimension of linear systems, with base points of multiplicity 2 and 3, on an Hirzebruck surface.

In this paper we study the topology of the spaces Hol(M,P{n},k) of (basepoint preserving) holomorphic maps of a given degree k from a Riemann surface M of genus g>0 into the n-th complex projective space P{n}, n>0. Using symmetric products…

Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices under *congruence are given over an algebraically closed field…

We classify the group of birational automorphisms of Hilbert schemes of points on algebraic K3 surfaces of Picard rank one. We study whether these automorphisms are symplectic or non-symplectic and if there exists a hyperk\"ahler birational…

We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS$_{3}$ algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis…