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A t-cover of the finite projective space PG(d,q) is a setS of t-dimensional subspaces such that any point of PG(d,q) is contained in at least one element ofS. In Theorem 1 a lower bound for the cardinality of a t-coverS in PG(d,q) is obtained and in Theorem 2 it is shown that this bound is best possible for all positive integers t,d and for any prime-power q.  相似文献   

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A t-cover of a finite projective space ℙ is a set of t-dimensional subspaces covering all points of ℙ. Beutelspacher [1] constructed examples of t-covers and proved that his examples are of minimal cardinality. We shall show that all examples of minimal cardinality “look like” the examples of Beutelspacher.  相似文献   

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We construct a crystallization of the real projective space whose associated contracted complex is minimal with respect to the number of n-simplexes. Then we compute the regular genus of , which is the minimum genus of a closed connected surface into which a crystallization of regularly embeds. Received: 7 February 2007  相似文献   

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In this paper, we consider new results on (k, n)-caps with n > 2. We provide a lower bound on the size of such caps. Furthermore, we generalize two product constructions for (k, 2)-caps to caps with larger n. We give explicit constructions for good caps with small n. In particular, we determine the largest size of a (k, 3)-cap in PG(3, 5), which turns out to be 44. The results on caps in PG(3, 5) provide a solution to four of the eight open instances of the main coding theory problem for q = 5 and k = 4.  相似文献   

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We introduce the notion of a Barbilian space of a projective lattice geometry in order to investigate the relationship between lattice-geometric properties and the properties of point-hyperplane structures associated with. We obtain a characterization of those projective lattice geometries, the Barbilian space of which is a Veldkamp space.  相似文献   

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A skewprojective space is a generalization of both groups and projective spaces. It is desarguesian if it is the space of infinity of a suitable skewaffine space. Especially a projective space is desarguesian in the sense cited above iff it is desarguesian in the usual sense. As a generalization of the well known fact that a proper subspace of a projective space is always desarguesian we establish a large class of skew-projective spaces also possessing this property.Dedicated to Günter Pickert on his 80th birthday  相似文献   

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In this paper we extend the results on projective changes of complex Finsler metrics obtained in Aldea and Munteanu (2012) [3], by the study of projective curvature invariants of a complex Finsler space. By means of these invariants, the notion of complex Douglas space is then defined. A special approach is devoted to the obtaining of equivalence conditions for a complex Finsler space to be a Douglas one. It is shown that any weakly Kähler Douglas space is a complex Berwald space. A projective curvature invariant of Weyl type characterizes complex Berwald spaces. These must be either purely Hermitian of constant holomorphic curvature, or non-purely Hermitian of vanishing holomorphic curvature. Locally projectively flat complex Finsler metrics are also studied.  相似文献   

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We use explicit results on modular forms (Mui?, Ramanujan J 27:188–208, 2012) via uniformization theory to obtain embeddings of modular curves and more generally of compact Riemann surfaces attached to Fuchsian groups of the first kind in certain projective spaces. We obtain families of embeddings which vary smoothly with respect to a parameter in the upper-half plane. We study local expression for the divisors attached to the maps in the family.  相似文献   

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The rate of a standard gradedK-algebraR is a measure of the growth of the shifts in a minimal free resolution ofK as anR-module. It is known that rate(R)=1 if and only ifR is Koszul and that rate(R) ≥m(I)−1 wherem(I) denotes the highest degree of a generator of the defining idealI ofR. We show that the rate of the coordinate ring of certain sets of pointsX of the projective space P n is equal tom(I)−1. This extends a theorem of Kempf. We study also the rate of algebras defined by a space of forms of some fixed degreed and of small codimension.  相似文献   

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