In this paper, we generalise the results of [5] on the reduction theory of binary forms, which describe positive zero-cycles in P, to positive zero-cycles (or point clusters) in projective spaces of arbitrary dimension. This should have applications to more general projective varieties in P, by associating a suitable positive zerocycle to them in an PGL(n + 1)-invariant way. We discuss this in ...

Evaluators and researchers often have to deal with situations in which conventional research tools are impossible to use, either because of the characteristics of a population or unclear research variables. This paper presents a technique that succeeds in overcoming this kind of problem--a projective technique, but one that differs from the usual approach to projective techniques. The approach ...

During recent years, several studies have revealed that human-dog relationships are based on a well-established and complex bond. There is now evidence suggesting that the dog-human affectional bond can be characterized as an "attachment". The present study investigated possible association between the owners' attachment profile assessed throughout a new semi-projective test (the 9 Attachment P...

We consider those projective bundles (or Brauer-Severi varieties) over an abelian variety that are homogeneous, i.e., invariant under translation. We describe the structure of these bundles in terms of projective representations of commutative group schemes; the irreducible bundles correspond to Heisenberg groups and their standard representations. Our results extend those of Mukai on semi-homo...

In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the weighted Weak Factorization Theorems of nonsingular projective varieties and more generally projective varieties with finite quotient singularities. Along the way, we will also mention some progresses on birational geom...

In this paper, the fuzzy counterparts and intuitionistic of central collineations defined in classical projective planes are planes, respectively. The properties left invariant under characterized depending on base point, line membership degrees plane plane.

In this paper the notion of an M -th order invariant bilinear differential pairing is introduced and a formal definition is given. If the manifold has an AHS structure, then various first order pairings are constructed. This yields a classification of all first order invariant bilinear differential pairings on homogeneous spaces with an AHS structure except for certain totally degenerate cases....

Let G be a connected Lie group acting by algebra automorphisms on a finite-dimensional complex central simple algebra A. The algebra A is isomorphic to the endomorphism algebra of a projective representation V of G. We study the invariant subalgebras of A. In particular, we show that if V is irreducible, then the invariant subalgebras appear in dual pairs arising from factorizations of V . We a...

We study hypersurfaces of complex projective manifolds which are invariant by a foliation, or more generally which are solutions to a Pfaff equation. We bound their degree using classical results on logarithmic forms.

We show that for smooth complex projective varieties the most general combinations of chern numbers that are invariant under the K-equivalence relation consist of the complex elliptic genera. §