共查询到20条相似文献,搜索用时 15 毫秒
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We initiate the study of representations of elementary abelian p-groups via restrictions to truncated polynomial subalgebras of the group algebra generated by r nilpotent elements, . We introduce new geometric invariants based on the behavior of modules upon restrictions to such subalgebras. We also introduce modules of constant radical and socle type generalizing modules of constant Jordan type and provide several general constructions of modules with these properties. We show that modules of constant radical and socle type lead to families of algebraic vector bundles on Grassmannians and illustrate our theory with numerous examples. 相似文献
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Iva Stavrov 《Differential Geometry and its Applications》2005,23(2):128-148
A pseudo-Riemannian manifold is said to be spacelike Jordan IP if the Jordan normal form of the skew-symmetric curvature operator depends upon the point of the manifold, but not upon the particular spacelike 2-plane in the tangent bundle at that point. We use methods of algebraic topology to classify connected spacelike Jordan IP pseudo-Riemannian manifolds of signature (p,q), where q?11, and where the set {q,…,q+p} does not contain a power of 2. 相似文献
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We introduce a notion of regularity for coherent sheaves on Grassmannians of lines. We use this notion to prove some extension of Evans–Griffith criterion to characterize direct sums of line bundles. We also give, in the line of previous results by Costa and Miró-Roig, a cohomological characterization of exterior and symmetric powers of the universal bundles of the Grassmannian. 相似文献
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The space of admissible particle velocities is assumed to be a four-dimensional nonholonomic distribution on a principal or associated bundle. Equations for the horizontal geodesics of this distribution coincide with the equations of motion of charged particles in general relativity theory. It is proved that, if the Lie group of the standard model of elementary particle physics is augmented by the 4-torus, then the wave functions are eigenfunctions of charge operators and the horizontal lift does not depend on the coupling constants. These wave functions satisfy the well-known Dirac equation and its generalizations. For such wave functions, the topological quantization of electric, lepton, and baryon charges takes place. 相似文献
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Corrado Zanella 《Discrete Mathematics》2006,306(15):1805-1811
In this paper the most natural questions concerning the blocking sets in the line Grassmannian of PG(n,q) are partially answered. In particular, the following Bose-Burton type theorems are proved: if n is odd or n=4, then the blocking sets of minimum size are precisely the linear complexes with singular subspace of minimum dimension. 相似文献
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The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these
spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations
of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological)
theta functions for line bundles over constant, commutative deformations. The second case is a calculation of the cohomologies
of non-commutative deformations of degree-zero line bundles. 相似文献
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Giorgio Ottaviani 《Annali di Matematica Pura ed Applicata》1989,155(1):317-341
Summary
In this paper we prove that a vector bundle E on a grassmannian (resp. on a quadric) splits as a direct sum of line bundles if and only if certain cohomology groups involving E and the quotient bundle (resp. the spinor bundle) are zero. When rank E=2 a better criterion is obtained considering only finitely many suitably chosen cohomology groups.This paper has been written while the author was enrolled in the Research Doctorate of the University of Florence. Partially supported by MPI 40% funds. 相似文献
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Iva Stavrov 《Topology and its Applications》2007,154(12):2391-2411
Methods from algebraic topology are often used to relate the algebraic properties of the Riemann curvature tensor to the geometry and topology of the underlying manifold. This paper provides a study of vector bundles over Grassmannians suitable for analyzing the spectral geometry of the Riemann tensor. Primarily, we study bundles over Grk(m), k?3, which are sub-bundles of the trivial bundle of rank m. 相似文献
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Leonardo Biliotti Anna Gori 《Transactions of the American Mathematical Society》2005,357(5):1731-1751
The main result of the paper is the complete classification of the compact connected Lie groups acting coisotropically on complex Grassmannians. This is used to determine the polar actions on the same manifolds.
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Vincenzo Ancona 《Annali di Matematica Pura ed Applicata》1987,149(1):153-164
Summary
We prove some vanishing and nonvanishing theorems for numerically effective line bundles, generalizing to complex spaces and morphisms between complex spaces results of Kawamata, Viehweg and Shokurov.A Guido Zappa per il suo settantesimo compleannoSupported by SFB 170 «Geometrie und Analysis», Göttingen (FRG), and by Ministero Pubblica Istruzione. 相似文献
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LetX be a smooth irreducible projective variety over an algebraically closed fieldK andE a vector bundle onX. We prove that, if dimX ≥ 1, there exist a smooth irreducible projective varietyZ overK, a surjective separable morphismf:Z →X which is finite outside an algebraic subset of codimension ≥ 3 inX and a line bundleL onX such that the direct image ofL byf is isomorphic toE. WhenX is a curve, we show thatZ, f, L can be so chosen thatf is finite and the canonical mapH
1(Z, O) →H
1(X, EndE) is surjective.
Dedicated to the memory of Professor K G Ramanathan 相似文献
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We give a pinching condition for compact minimal hypersurfaces in complex two-plane Grassmannians G 2(? m+2) in terms of sectional curvature and the squared norm of the shape operator. 相似文献
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We prove that there does not exist any semi-parallel real hypersurface in complex two-plane Grassmannians. With this result, the nonexistence of recurrent real hypersurfaces in complex two-plane Grassmannians can also be proved. 相似文献
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Young Jin Suh 《Acta Mathematica Hungarica》2006,112(1-2):89-102
Summary We introduce the notion of recurrent shape operator for a real hypersurface M in the complex two-plane Grassmannians G2(Cm+2) and give a non-existence property of real hypersurfaces in G2(Cm+2) with the recurrent shape operator. 相似文献
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Xiaoxiang Jiao 《Israel Journal of Mathematics》2008,163(1):45-60
In this paper we consider pseudo-holomorphic curves in complex Grassmiannians. Let φ 0, φ 1, ?, $\varphi _{\alpha _0 } $ : S 2 → G k,n be a linearly full non-degenerate pseudo-holomorphic harmonic sequence, and let degφα and K α be the degree and the Gauss curvature of φα (α = 0, 1, ?, α 0) respectively. Assume that φ 0, φ 1, ?, $\varphi _{\alpha _0 } $ is totally unramified. Then we prove that (i) degφα for all α = 0, 1, ?, α 0; (ii) $K_\alpha = \tfrac{4}{{k(\alpha _0 + 2\alpha (\alpha _0 - \alpha ))}}$ if K α is constant for some α = 0, 1, ?, α 0,. We also give some conditions for pseudo-holomorphic curves with constant Kähler angle in complex Grassmiannians to be of constant curvature. 相似文献