相关论文: Flags in zero dimensional complete intersections a…

The study of symmetries in the realm of manifolds can be approached in two different ways. On one hand, Killing vector fields on a (pseudo-)Riemannian manifold correspond to the directions of local isometries within it. On the other hand,…

In this paper we outline some aspects of nonabelian gauged linear sigma models. First, we review how partial flag manifolds (generalizing Grassmannians) are described physically by nonabelian gauged linear sigma models, paying attention to…

We explicitly characterize when the Milnor number at the origin of a polynomial or power series (over an algebraically closed field k of arbitrary characteristic) is the minimum of all polynomials with the same Newton diagram, which…

We study moduli spaces of a class of three dimensional N=4 gauge theories which are in one-to-one correspondence with a certain set of ordered pairs of integer partitions. It was found that these theories can be realised on brane intervals…

We study the generalized Galois numbers which count flags of length r in N-dimensional vector spaces over finite fields. We prove that the coefficients of those polynomials are asymptotically Gaussian normally distributed as N becomes…

In a spirit of Givental's constructions Batyrev, Ciocan-Fontanine, Kim, and van Straten suggested Landau--Ginzburg models for smooth Fano complete intersections in Grassmannians and partial flag varieties as certain complete intersections…

We use recent results about linking the number of zeros on algebraic varieties over $\mathbb{C}$, defined by polynomials with integer coefficients, and on their reductions modulo sufficiently large primes to study congruences with products…

Given a zero-dimensional Gorenstein algebra $\mathbb{B}$ and two syzygies between two elements $f_1,f_2\in\mathbb{B}$, one constructs a double complex of $\mathbb{B}$-modules, ${\cal G}_\mathbb{B},$ called the small Gobelin. We describe an…

The paper is devoted to a computation of the Lie superalgebras of holomorphic vector fields on isotropic flag supermanifolds of maximal type corresponding to the Lie superalgebras $\mathfrak{osp}_{2m|2n}(\mathbb C)$ and…

In complex vector spaces maximal sets of equiangular lines, known as SICs, are related to real quadratic number fields in a dimension dependent way. If the dimension is of the form $n^2+3$ the base field has a fundamental unit of negative…

An old result of the first author and David Lieberman says that if a compact Kaehler manifold X admits a holomorphic vector field V having at least one zero, then the Dolbeault cohomology algebra H^*(X, \Omega^*) of X is isomorphic with the…

Given a unit vector field on a closed Euclidean hypersurface, we define a map from the hypersurface to a sphere in the Euclidean space. This application allows us to exhibit a list of topological invariants which combines the second…

A classification of double flag varieties of complexity 0 and 1 is obtained. An application of this problem to decomposing tensor products of irreducible representations of semisimple Lie groups is considered.

The Semiinfinite Flag Space appeared in the works of B.Feigin and E.Frenkel, and under different disguises was found by V.Drinfeld and G.Lusztig in the early 80-s. Another recent discovery (Beilinson-Drinfeld Grassmannian) turned out to…

In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these…

This work investigates invariants, including the GSV-index, the local Euler obstruction, and the Brasselet number, within the context of isolated complete intersection singularities (ICIS). The goal is to forge connections among these…

We consider Schubert problems with respect to flags osculating the rational normal curve. These problems are of special interest when the osculation points are all real -- in this case, for zero-dimensional Schubert problems, the solutions…

The goal of the paper is two-fold. At first, we attempt to give a survey of some recent applications of symmetric polynomials and divided differences to intersection theory. We discuss: polynomials universally supported on degeneracy loci;…

The vector algebra and calculus are frequently used in many branches of Physics, for example, classical mechanics, electromagnetic theory, Astrophysics, Spectroscopy, etc. Important vector identities with the help of Levi-Civita symbols and…

In a previous paper we defined the concept of an affinized projective variety and its associated Hilbert series. We computed the Hilbert series for varieties associated to quadratic monomial ideals. In this paper we show how to apply these…