共查询到20条相似文献,搜索用时 15 毫秒
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We study the complex symplectic structure of the quiver varieties corresponding to the moduli spaces of SU(2) instantons on both commutative and non-commutative R4. We identify global Darboux coordinates and quadratic Hamiltonians on classical phase spaces for which these quiver varieties are natural completions. We also show that the group of non-commutative symplectomorphisms of the corresponding path algebra acts transitively on the moduli spaces of non-commutative instantons. This paper should be viewed as a step towards extending known results for Calogero–Moser spaces to the instanton moduli spaces. 相似文献
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We exhibit tight contact structures on 3-manifolds that do not admit any symplectic fillings.
Oblatum 7-XII-2000 & 14-XI-2001?Published online: 9 April 2002 相似文献
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An approach to a natural geometry of moduli spaces of symplectic structures is presented.
Received: 21 March 2002 / Revised version: 28 August 2002
This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG). 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
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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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Given a field 𝕂 of characteristic 2 and an integer n ≥ 2, let W(2n ? 1, 𝕂) be the symplectic polar space defined in PG(2n ? 1, 𝕂) by a non-degenerate alternating form of V(2n, 𝕂) and let Q(2n, 𝕂) be the quadric of PG(2n, 𝕂) associated to a non-singular quadratic form of Witt index n. In the literature it is often claimed that W(2n ? 1, 𝕂) ? Q(2n, 𝕂). This is true when 𝕂 is perfect, but false otherwise. In this article, we modify the previous claim in order to obtain a statement that is correct for any field of characteristic 2. Explicitly, we prove that W(2n ? 1, 𝕂) is indeed isomorphic to a non-singular quadric Q, but when 𝕂 is non-perfect the nucleus of Q has vector dimension greater than 1. So, in this case, Q(2n, 𝕂) is a proper subgeometry of W(2n ? 1, 𝕂). We show that, in spite of this fact, W(2n ? 1, 𝕂) can be embedded in Q(2n, 𝕂) as a subgeometry and that this embedding induces a full embedding of the dual DW(2n ? 1, 𝕂) of W(2n ? 1, 𝕂) into the dual DQ(2n, 𝕂) of Q(2n, 𝕂). 相似文献
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Let (V, Ω) be a symplectic vector space and let \({\phi : M \rightarrow V}\) be a symplectic immersion. We show that \({\phi(M) \subset V}\) is locally an extrinsic symplectic symmetric space (e.s.s.s.) in the sense of Cahen et al. (J Geom Phys 59(4):409f?b-425, 2009) if and only if the second fundamental form of \({\phi}\) is parallel. Furthermore, we show that any symmetric space, which admits an immersion as an e.s.s.s., also admits a full such immersion, i.e., such that \({\phi(M)}\) is not contained in a proper affine subspace of V, and this immersion is unique up to affine equivalence. Moreover, we show that any extrinsic symplectic immersion of M factors through to the full one by a symplectic reduction of the ambient space. In particular, this shows that the full immersion is characterized by having an ambient space V of minimal dimension. 相似文献
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Sangyop Lee 《Mathematische Zeitschrift》2011,267(3-4):781-802
We show that if M is a hyperbolic 3-manifold with ?M a torus such that M(r 1) is a lens space and M(r 2) is toroidal, then ??(r 1, r 2) ?? 4. 相似文献
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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
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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
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Alvaro Pelayo 《Proceedings of the American Mathematical Society》2007,135(1):277-288
We compute the homotopy type of the space of -equivariant symplectic embeddings from the standard -dimensional ball of some fixed radius into a -dimensional symplectic-toric manifold , and use this computation to define a -valued step function on which is an invariant of the symplectic-toric type of . We conclude with a discussion of the partially equivariant case of this result.
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For certain classes of isolated complex surface singularities, it is shown that there exist infinitely many distinct topological
types of minimal symplectic fillings of the link of the singularity. 相似文献
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Kouyemon Iriye 《Proceedings of the American Mathematical Society》2008,136(2):727-733
We prove that is stably indecomposable if or .