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1.
Bieliavsky introduced and investigated a class of symplectic symmetric spaces, that is, symmetric spaces endowed with a symplectic structure invariant with respect to symmetries. The theory of symmetric spaces has essential and interesting generalizations due to the fundamental work of Gray and Wolf continued by many researchers. Therefore, we ask a question about possible symplectic versions of such theory. In this paper we do obtain such generalization, and, in particular, give a list of all symplectic 3-symmetric manifolds with simple groups of transvections. We also show a method of constructing semisimple (noncompact) symplectic \(k\) -symmetric spaces from a given (compact) Kähler k-symmetric space. 相似文献
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Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally
factorial, with the exception of symmetric products of a K3 or abelian surface and the class of moduli spaces found by O’Grady.
Consequently, since singular moduli space that do not belong to these exceptional cases have singularities in codimension
≥4 they do no admit projective symplectic resolutions.
A la mémoire de Joseph Le Potier
Mathematics Subject Classification (1991) 14J60, 14D20, 14J28, 32J27 相似文献
4.
Rui Albuquerque 《Annali di Matematica Pura ed Applicata》2009,188(3):429-443
We consider some classical fibre bundles furnished with almost complex structures of twistor type, deduce their integrability
in some cases and study self-holomorphic sections of the general twistor space, with which we define a new moduli space of complex structures. We also recall the
theory of flag manifolds to study the Siegel domain and other domains alike, which are the fibres of various symplectic twistor
spaces. We prove that they are all Stein. In the context of a Riemann surface, with its canonical symplectic-metric connection
and local structure equations, the moduli space is studied again. 相似文献
5.
Lenka Zalabová 《Annals of Global Analysis and Geometry》2010,37(2):125-141
We study here systems of symmetries on |1|-graded parabolic geometries. We are interested in smooth systems of symmetries,
and we discuss non-flat homogeneous |1|-graded geometries. We show the existence of an invariant admissible affine connection
under quite weak condition on the system. 相似文献
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Let G be a semisimple Lie group, g its Lie algebra. For any symmetric space M over G we construct a new (deformed) multiplication in the space A of smooth functions on M. This multiplication is invariant under the action of the Drinfeld-Jimbo quantum group Uhg and is commutative with respect to an involutive operator
. Such a multiplication is unique. Let M be a kählerian symmetric space with the canonical Poisson structure. Then we construct a Uhg-invariant multiplication in A which depends on two parameters and is a quantization of that structure. 相似文献
7.
Fabio Podestà 《Annali di Matematica Pura ed Applicata》1989,154(1):371-383
Sunto In questo lavoro l'autore estende la nozione di simmetria al caso di una varietà reale C dotata di una connessione proiettiva normale, introducendo la classe degli spazi proiettivamente simmetrici. L'autore prova che ogni spazio proiettivamente simmetrico p-iperbolico è proiettivamente equivalente ad uno spazio Riemanniano simmetrico di Einstein con curvatura negativa. Infine l'autore prova che una varietà Riemanniana completa n-dimensionale (n>/2) localmente affinemente simmetrica, proiettivamente simmetrica in senso proprio e proiettivamente omogenea è proiettivamente equivalente alla sfera Sn oppure allo spazio proiettivo realeRP
n. 相似文献
8.
V. N. Berestovskii 《Siberian Mathematical Journal》1985,26(2):159-170
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Paolo Lisca 《Transactions of the American Mathematical Society》2008,360(2):765-799
Let be the contact structure naturally induced on the lens space by the standard contact structure on the three-sphere . We obtain a complete classification of the symplectic fillings of up to orientation-preserving diffeomorphisms. In view of our results, we formulate a conjecture on the diffeomorphism types of the smoothings of complex two-dimensional cyclic quotient singularities.
12.
Simon Gindikin Bernhard Krö tz 《Transactions of the American Mathematical Society》2002,354(8):3299-3327
In this paper we define a distinguished boundary for the complex crowns of non-compact Riemannian symmetric spaces . The basic result is that affine symmetric spaces of can appear as a component of this boundary if and only if they are non-compactly causal symmetric spaces.
13.
Hiêú Nguyêñ 《Transformation Groups》1997,2(4):351-374
LetG be a connected, simply-connected, real semisimple Lie group andK a maximal compactly embedded subgroup ofG such thatD=G/K is a hermitian symmetric space. Consider the principal fiber bundleM=G/K
s
G/K, whereK
s
is the semisimple part ofK=K
s
·Z
K
0
andZ
K
0
is the connected center ofK. The natural action ofG onM extends to an action ofG
1=G×Z
K
0
. We prove as the main result thatM is weakly symmetric with respect toG
1 and complex conjugation. In the case whereD is an irreducible classical bounded symmetric domain andG is a classical matrix Lie group under a suitable quotient, we provide an explicit construction ofM=D×S
1 and determine a one-parameter family of Riemannian metrics onM invariant underG
1. Furthermore,M is irreducible with respect to . As a result, this provides new examples of weakly symmetric spaces that are nonsymmetric, including those already discovered by Selberg (cf. [M]) for the symplectic case and Berndt and Vanhecke [BV1] for the rank-one case.Research partially supported by an NSF grant. The author wishes to thank the International Erwin Schroedinger Institute for its hospitality during the preparation of this paper. 相似文献
14.
O. I. Mokhov 《Functional Analysis and Its Applications》1991,25(2):136-137
Scientific Industrial Association, All-Union Scientific Research Institute of Physicotechnical and Radiotechnical Measurements. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 2, pp. 65–67, April–June, 1991. 相似文献
15.
Fully symmetric operator spaces 总被引:4,自引:0,他引:4
Peter G. Dodds Theresa K. Dodds Ben de Pagter 《Integral Equations and Operator Theory》1992,15(6):942-972
It is shown that certain interpolation theorems for non-commutative symmetric operator spaces can be deduced from their commutative versions. A principal tool is a refinement of the notion of Schmidt decomposition of a measurable operator affiliated with a given semi-finite von Neumann algebra.Research supported by A.R.C. 相似文献
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We extend Ferus?? characterization of extrinsic symmetric spaces to ambient spaces with indefinite inner products. 相似文献