Related papers: The BGG Complex on Projective Space
For curved projective manifolds we introduce a notion of a normal tractor frame field, based around any point. This leads to canonical systems of (redundant) coordinates that generalise the usual homogeneous coordinates on projective space.…
Non-trivial examples of generalized paracomplex structures (in the sense of the generalized geometry \`a la Hitchin) are constructed applying the twistor space construction scheme.
On a symplectic manifold, there is a natural elliptic complex replacing the de Rham complex. It can be coupled to a vector bundle with connection and, when the curvature of this connection is constrained to be a multiple of the symplectic…
A simple scheme to express the Mellin transform of $D$-dimensional Euclidean conformal bootstrap equation is presented by relating conformal blocks to a Gauss-Grassmann (GG) system due to Gelfand-Graev, associated to conformal integrals,…
In this paper, we construct discrete versions of some Bernstein-Gelfand-Gelfand (BGG) complexes, i.e., the Hessian and the divdiv complexes, on triangulations in 2D and 3D. The sequences consist of finite elements with local polynomial…
Simple constructions are given for finite semifields that include as special cases both old semifields and recently constructed semifields.
Let $G$ be a semisimple Lie group with finite center, $K\subset G$ a maximal compact subgroup, and $P\subset G$ a parabolic subgroup. Following ideas of P.Y.\ Gaillard, one may use $G$-invariant differential forms on $G/K\times G/P$ to…
We express total set of rational Gromov-Witten invariants of projective spaces via periods of variations of semi-infinite Hodge structure associated with their mirror partners.
An expository description of smooth cubic curves in the real or complex projective plane.
We develop a new method to construct explicit, regular minimal surfaces in Euclidean space that are defined on the entire complex plane with controlled geometry. More precisely we show that for a large class of planar curves $(x(t), y(t))$…
Based on a calibration argument, we prove a Bernstein type theorem for entire minimal graphs over Gauss space $\mathbb{G}^n$ by a simple proof.
We show a way of constructing projectional skeletons using the concept of rich families in Banach spaces which admit a projectional generator. Our next result is that a Banach space $X$ is Asplund and weakly compactly generated if and only…
We review the basic elements of the Minimal Geometric Deformation approach in details. This method has been successfully used to generate brane-world configurations from general relativistic perfect fluid solutions.
The existence of the Gorenstein projective precovers over arbitrary rings is an open question. It is known that if the ring has finite Gorenstein global dimension, then every module has a Gorenstein projective precover. We prove here a…
We construct a class of super-reflexive complementably minimal spaces, and study uniformly convex distortions of the norm on Hilbert space by using methods of complex interpolation.
For $1<p<\infty$, we emulate the Bergman projection on Reinhardt domains by using a Banach-space basis of $L^p$-Bergman space. The construction gives an integral kernel generalizing the ($L^2$) Bergman kernel. The operator defined by the…
We construct affine spaces, projective spaces and grassmannians in the ca\-te\-gory of ringed spaces. We show how finite posets and sheaves of rings on them appear in a natural way.
In this article we find some sufficient conditions for the set in the Bilateral Grand Lebesgue Space to be compact set. We consider applications into numerical methods and in the basis problem.
The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…