Chen and Ruan [6] defined a very interesting cohomology theoryChen-Ruan orbifold cohomology. The primary objective of this paper is to compute the Chen-Ruan orbifold cohomology of the weighted projective spaces, one of the most important space used in physics. The classical tools (orbifold cohomology defined by Chen and Ruan, toric varieties, the localization technique) which have been proved t...

We calculate the small quantum orbifold cohomology of arbitrary weighted projective spaces. We generalize Givental’s heuristic argument, which relates small quantum cohomology to S-equivariant Floer cohomology of loop space, to weighted projective spaces and use this to conjecture an explicit formula for the small J-function, a generating function for certain genuszero Gromov–Witten invariants....

In this paper, we extend the definition of the Nathanson height from points in projective spaces over Fp to points in projective spaces over arbitrary finite fields. If [a0 : . . . : an] ∈ P(Fp), then the Nathanson height is hp([a0 : a1 : . . . : ad]) = min b∈Fp d ∑ i=0 H(bai) where H(ai) = |N(ai)|+p(deg(ai)−1) with N the field norm and |N(ai)| the element of {0, 1, . . . , p− 1} congruent to N...

The spinor representation is developed and used to investigate minimal surfaces in R with embedded planar ends. The moduli spaces of planar-ended minimal spheres and real projective planes are determined, and new families of minimal tori and Klein bottles are given. These surfaces compactify in S to yield surfaces critical for the Möbius invariant squared mean curvature functional W . On the ot...

1.) Pm(C), 2.) smooth abelian families, 3.) manifolds with universal covering Bm(C). Here Bm(C) denotes the ball in C , the non compact dual of Pm(C) in the sense of hermitian symmetric spaces. The second point inlcudes the flat case of an abelian manifold. Any compact Riemann surface admits a holomorphic normal projective connection, this is the famous uniformization theorem. Kobayashi and Och...

A Fano variety is a projective variety whose anticanonical class is ample. A 2–dimensional Fano variety is called a Del Pezzo surface. In higher dimensions, attention originally centered on smooth Fano 3–folds, but singular Fano varieties are also of considerable interest in connection with the minimal model program. The existence of Kähler–Einstein metrics on Fano varieties has also been explo...

A projective Reed–Muller (PRM) code, obtained by modifying a Reed–Muller code with respect to a projective space, is a doubly extended Reed–Solomon code when the dimension of the related projective space is equal to 1. The minimum distance and the dual code of a PRM code are known, and some decoding examples have been presented for low-dimensional projective spaces. In this study, we construct ...

In this paper, we introduce a novel pictorial approach for solving problems in n-dimensional Euclidean spaces called the n-dimensional projective approach. The projective approach is based on a hierarchical and modular architecture, where its ground module is rooted on geometrical concepts. The result is an effective and consistent spatial approach able to solve problems in ndimensional spaces ...

Many classes of projective algebraic varieties can be studied in terms of graded rings. Gorenstein graded rings in small codimension have been studied recently from an algebraic point of view, but the geometric meaning of the resulting structures is still relatively poorly understood. We discuss here the weighted projective analogs of homogeneous spaces such as the Grassmannian Gr(2, 5) and ort...