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51.
A modular symbol is the fundamental class of a totally geodesic submanifold embedded in a locally Riemannian symmetric space , which is defined by a subsymmetric space . In this paper, we consider the modular symbol defined by a semisimple symmetric pair (G,G'), and prove a vanishing theorem with respect to the -component in the Matsushima-Murakami formula based on the discretely decomposable theorem of the restriction . In particular, we determine explicitly the middle Hodge components of certain totally real modular symbols on the locally
Hermitian symmetric spaces of type IV.
Received: December 8, 1996 相似文献
52.
Christian Meyer 《Mathematische Nachrichten》2003,259(1):66-73
We will examine the arithmetic of some of the members of a pencil of symmetric quintics in projective 4‐space. We will give evidence for the modularity of some of the exceptional members (even the non‐rigid ones) and give a proof in one rigid case. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
53.
We study residues on a complete toric variety X, which are defined in terms of the homogeneous coordinate ring of X.We first prove a global transformation law for toric residues. When the fan of the toric variety has a simplicial cone of maximal dimension, we can produce an element with toric residue equal to 1. We also show that in certain situations, the toric residue is an isomorphism on an appropriate graded piece of the quotient ring. When X is simplicial, we prove that the toric residue is a sum of local residues. In the case of equal degrees, we also show how to represent X as a quotient (Y\{0})/C* such that the toric residue becomes the local residue at 0 in Y. 相似文献
54.
The Chow/Van der Waerden approach to algebraic cycles via resultants is used to give a purely algebraic proof for the algebraicity of the complex suspension. The algebraicity of the join pairing on Chow varieties then follows. The approach implies a more algebraic proof of Lawson's complex suspension theorem in characteristic 0. The continuity of the action of the linear isometries operad on the group completion of the stable Chow variety is a consequence.
55.
We show several estimates on the probability distribution of some data at points in real complete intersection varieties: norms of real affine solutions, condition number of real solution of real systems of multi-variate polynomial equations and convergence radius of Newton's operator for under-determined system of multi-variate polynomial equations. 相似文献
56.
We prove that the cone over a Schubert variety inG/P (P being a maximal parabolic subgroup of classical type) is normal by exhibiting a 2-regular sequence inR(w) (the homogeneous coordinate ring of the Schubert varietyX(w) inG/P under the canonical protective embeddingG/P ⊂→ (p (H° G/P,L)),L being the ample generator of (PicG/P), which vanishes on the singular locus ofX(w). We also prove the surjectivity ofH° (G/Q, L) H° (X(w), L), whereQ is a classical parabolic subgroup (not necessarily maximal) ofG andL is an ample line bundle onG/Q. 相似文献
57.
58.
Margherita Barile Gennady Lyubeznik 《Proceedings of the American Mathematical Society》2005,133(11):3199-3209
We describe a class of toric varieties which are set-theoretic complete intersections only over fields of one positive characteristic .
59.
Valentina Rossi 《Applied Categorical Structures》2006,14(4):291-311
Given a regular Gumm category such that any regular epimorphism is effective for descent, we prove that any Birkhoff subcategory in gives rise to an admissible Galois structure. This result allows one to consider some new applications of the categorical Galois theory in the context of topological algebras. Given a regular Mal’cev category , we first characterize the coverings of the Galois structure induced by the subcategory of the abelian objects in . Then we consider as a subcategory of the category of the equivalence relations in , and we characterize the coverings of the corresponding Galois structure . By composing the Galois structures and we obtain the Galois structure induced by as a subcategory of . We give the characterization of the -coverings in terms of the coverings of and . 相似文献
60.
Yoshihiro Ochi 《Proceedings of the American Mathematical Society》2006,134(1):31-37
We prove that for any abelian variety defined over a number field that is not isogenous to a product of CM elliptic curves, the pontrjagin dual of the Selmer group of the abelian variety over the trivializing extension has no nonzero pseudo-null submodules.