共查询到20条相似文献,搜索用时 15 毫秒
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We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases
one can “hear” the weights of a weighted projective space. 相似文献
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Kwang Sung Park 《Mathematische Annalen》1989,284(3):503-513
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Motivated by the work of Crapo and Rota [6] on the lifting of a projective complex, we introduce a class of invariant operations associated to integral-weighted graphs, which we call graphical operations. Such operations generalize the sixth harmonic of a quadranguler set on a projective line. We determine the expansion of the graphical operations in terms of multi-linear bracket polynomials in a Grassmann-Cayley algebra. Reducibility and compositions of such invariant operations are also investigated with a number of examples.Supported by Courant Instructorship, New York University. 相似文献
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Christina Birkenhake 《manuscripta mathematica》1995,88(1):177-184
In the paper the propertiesÑ p (a generalization of the propertiesN p for projectively normal embeddings of projective varieties) are investigated for noncomplete Veronese embeddings. It is shown that the linear projection of a complete Veronese embedding ? n →? N from a general linear subspace of ? N of low dimension satisfies propertyÑ 0. Moreover, Theorem 3.1 yields an upper bound forp for a noncomplete Veronese embedding of the projective plane ?2 to satisfy propertyÑ p . 相似文献
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V. V. Konnov 《Journal of Mathematical Sciences》2007,142(5):2367-2376
In this paper, we construct a natural embedding \(\sigma :\mathbb{C}P_\mathbb{R}^{n} \to \mathbb{R}P^{n^2 + 2n} \) of the complex projective space ?P n considered as a 2n-dimensional, real-analytic manifold in the real projective space \(\mathbb{R}P^{n^2 + 2n} \). The image of the embedding σ is called the ?P n-surface. To construct the embedding, we consider two equivalent approaches. The first approach is based on properties of holomorphic bivectors in the realification of a complex vector space. This approach allows one to prove that a ?P-surface is a flat section of a Grassman manifold. In the second approach, we use the adjoint representation of the Lie group U(n + 1) and the canonical decomposition of the Lie algebra u(n). This approach allows one to state a gemetric characterization of the canonical decomposition of the Lie algebra u(n). Moreover, we study properties of the embedding constructed. We prove that this embedding determines the canonical Kähler structure on ?P ? n . In particular, the Fubini-Study metric is exactly the first fundamental form of the embedding and the complex structure on ?P ? n is completely defined by its second fundamental form; therefore, this embedding is said to be canonical. Moreover, we describe invariant and anti-invariant completely geodesic submanifolds of the complex projective space. 相似文献
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Dr. Ascher Wagner 《Mathematische Zeitschrift》1969,112(1):37-51
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USHA N BHOSLE 《Proceedings Mathematical Sciences》2013,123(3):331-344
We compute the cohomology of the Picard bundle on the desingularization $\tilde{J}^d(Y)$ of the compactified Jacobian of an irreducible nodal curve Y. We use it to compute the cohomology classes of the Brill–Noether loci in $\tilde{J}^d(Y)$ . We show that the moduli space M of morphisms of a fixed degree from Y to a projective space has a smooth compactification. As another application of the cohomology of the Picard bundle, we compute a top intersection number for the moduli space M confirming the Vafa–Intriligator formulae in the nodal case. 相似文献
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Norman L. Johnson 《Journal of Geometry》2003,76(1-2):110-182
New and old results on parallelisms of projective spaces are surveyed. 相似文献
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Alberto Canonaco 《Comptes Rendus Mathematique》2003,336(1):35-40
Beilinson's theorem [Funct. Anal. Appl. 12 (1978) 214–216], which describes the bounded derived category of coherent sheaves on , is extended to weighted projective spaces. This result is obtained by considering, instead of the usual category of coherent sheaves, a suitable category of graded coherent sheaves (which is equivalent in the case of ). To cite this article: A. Canonaco, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
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Starting with an abelian category
, a natural construction produces a category
such that, when
is an abelian category of vector spaces,
is the corresponding category of projective spaces. The process of forming the category
destroys abelianess, but not completely, and the precise measure of what remains of it gives the possibility to reconstruct
out from
, and allows to characterize categories of the form
, for an abelian
(projective categories). The characterization is given in terms of the notion of “Puppe exact category” and of an appropriate notion of “weak biproducts”. The proof of the characterization theorem relies on the theory of “additive relations”. 相似文献
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Edoardo Ballico 《Journal of Geometry》2004,81(1-2):1-4
Here we study finite unions, Y, of lines in a projective space PG(n, K). We prove that if K is an infinite field, Y spans PG(n, K) and a general hyperplane section of Y is not in linearly general position, then there exists at least one linear subspace M of PG(n, K) such that 2 dim(M) < n and M contains at least dim(M)+2 lines of Y.The author was partially supported by MIUR and GNSAGA of INdAM (Italy). 相似文献
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There are two definitions of Einstein-Finsler spaces introduced by Akbar-Zadeh, which we will show is equal along the integral curves of I-invariant projective vector fields. The sub-algebra of the C-projective vector fields, leaving the H-curvature invariant, has been studied extensively. Here we show on a closed Finsler space with negative definite Ricci curvature reduces to that of Killing vector fields. Moreover, if an Einstein-Finsler space admits such a projective vector field then the flag curvature is constant. Finally, a classification of compact isotropic mean Landsberg manifolds admitting certain projective vector fields is obtained with respect to the sign of Ricci curvature. 相似文献
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He Xin 《Annali dell'Universita di Ferrara》2018,64(2):449-463
On projective spaces of dimension \(d\ge 2\) defined over a field of positive characteristic we construct rank \(d+1\) uniform toric but non-homogeneous bundles, which do not exists in characteristic zero. These bundles are obtained by choosing suitable equivariant extensions of the Frobenius pullbacks of \(T_{\mathbb {P}^d}\) by a line bundle. 相似文献