Related papers: An introduction to varieties in weighted projectiv…
Given a holomorphic vector bundle $E:EX X$ over a compact K\"ahler manifold, one introduces twisted GW-invariants of $X$ replacing virtual fundamental cycles of moduli spaces of stable maps $f: \Sigma \to X$ by their cap-product with a…
The "dancing metric" is a pseudo-riemannian metric $\pmb{g}$ of signature $(2,2)$ on the space $M^4$ of non-incident point-line pairs in the real projective plane $\mathbb{RP}^2$. The null-curves of $(M^4,\pmb{g})$ are given by the "dancing…
We introduce a new definition of weighted Grassmann orbifolds. We study their several invariant $q$-cell structures and the orbifold singularities on these $q$-cells. We discuss when the integral cohomology of a weighted Grassmann orbifold…
We start from a new theory (discussed earlier) in which the arena for physics is not spacetime, but its straightforward extension-the so called Clifford space ($C$-space), a manifold of points, lines, areas, etc..; physical quantities are…
We present some basic elements of the theory of generalised Br\`{e}gman relative entropies over nonreflexive Banach spaces. Using nonlinear embeddings of Banach spaces together with the Euler--Legendre functions, this approach unifies two…
In this paper we provide some exact formulas for the projective dimension and the regularity of edge ideals associated to vertex weighted rooted forests and oriented cycles. As some consequences, we give some exact formulas for the depth of…
The aim of this paper is to study geometric properties of non-degenerate smooth projective varieties of small degree from a birational point of view. First, using the positivity property of double point divisors and the adjunction mappings,…
The issue of the transformations of units is treated, mainly, in a geometrical context. It is shown that Weyl-integrable geometry is a consistent framework for the formulation of the gravitational laws since the basic law on which this…
We introduce and explore a new concept of evasive subspace with respect to a collection of subspaces sharing a common dimension, most notably partial spreads. We show that this concept generalises known notions of subspace scatteredness and…
This paper is a self-contained presentation of certain aspects of the theory of weighted Sobolev spaces and elliptic operators on non-compact Riemannian manifolds. Specifically, we discuss (i) the standard and weighted Sobolev Embedding…
It is well known that $n$-dimensional projective group gives rise to a non-homogenous representation of the Lie algebra $sl(n+1)$ on the polynomial functions of the projective space. Using Shen's mixed product for Witt algebras (also known…
Motivated by the necessity to find exact solutions with the elliptic Weierstrass function of the Einstein's equations (see gr-qc/0105022),the present paper develops further the proposed approach in hep-th/0107231, concerning the s.c. cubic…
Determining the weight distributions of the projective Reed-Muller codes is a very hard problem and has been studied extensively in the literature. In this article, we provide an alternative proof of the second weight of the projective…
A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…
The multipullback quantization of complex projective spaces lacks the naive quantum CW-complex structure because the quantization of an embedding of the $n$-skeleton into the $(n+1)$-skeleton does not exist. To overcome this difficulty, we…
Kontsevich's formula for rational plane curves is a recursive relation for the number $N_d$ of degree $d$ rational curves in $\mathbb{P}^2$ passing through $3d-1$ general points. We provide two proofs of this recursion: the first more…
The Riemann-Roch Theorem is one of the cornerstones of algebraic geometry, connecting algebraic data (sheaf cohomology) with geometric ones (intersection theory). This survey paper provides a self-contained introduction and a complete proof…
We propose a quantization of coarse spaces and uniform Roe algebras. The objects are based on the quantum relations introduced by N. Weaver and require the choice of a represented von Neumann algebra. In the case of the diagonal inclusion…
The relationship between convex geometry and algebraic geometry has deep historical roots, tracing back to classical works in enumerative geometry. In this paper, we continue this theme by studying two interconnected problems regarding…
An important result in real algebraic geometry is the projection theorem: every projection of a semialgebraic set is again semialgebraic. This theorem and some of its conclusions lie at the basis of many other results, for example the…