A new approach to monopole moduli spaces

This paper focuses on a geometric structure defined by a system of closed exterior differential forms and develops a new approach to deformation problems of geometric structures. We obtain a criterion for unobstructed deformations from a cohomological point of view (Theorem 1.7). Further we show that under a cohomological condition, the moduli space of the geometric structures becomes a smooth manifold of finite dimension (Theorem 1.8). We apply our approach to the geometric structures such as Calabi–Yau, HyperKähler, G2 and Spin(7) structures and then obtain a unified construction of smooth moduli spaces of these four geometric structures. We generalize the Moser's stability theorem to provide a direct proof of the local Torelli type theorem in these four geometric structures (Theorem 1.10).

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Monopole moduli spaces for compact 3-manifolds

Mathematische Annalen ◽

10.1007/s002080050180 ◽

1998 ◽

Vol 311 (1) ◽

pp. 125-146 ◽

Cited By ~ 15

Author(s):

Marc Pauly

Keyword(s):

Moduli Spaces ◽

Monopole Moduli Spaces

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A note on monopole moduli spaces

Journal of Mathematical Physics ◽

10.1063/1.1590056 ◽

2003 ◽

Vol 44 (8) ◽

pp. 3517-3531 ◽

Cited By ~ 3

Author(s):

Michael K. Murray ◽

Michael A. Singer

Keyword(s):

Moduli Spaces ◽

Monopole Moduli Spaces

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A new approach for computing the geometry of the moduli spaces for a Calabi–Yau manifold

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8121/aa9e7a ◽

2018 ◽

Vol 51 (5) ◽

pp. 055403 ◽

Cited By ~ 6

Author(s):

Konstantin Aleshkin ◽

Alexander Belavin

Keyword(s):

Moduli Spaces ◽

New Approach

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Transverse hilbert schemes, bi-hamiltonian systems and hyperkähler geometry

The Quarterly Journal of Mathematics ◽

10.1093/qmath/haaa059 ◽

2020 ◽

Author(s):

Roger Bielawski

Keyword(s):

Hamiltonian Systems ◽

Moduli Spaces ◽

Hilbert Scheme ◽

Poisson Structures ◽

Hilbert Schemes ◽

Hyperkähler Manifolds ◽

Symplectic Surface ◽

Monopole Moduli Spaces ◽

Hyperkähler Geometry

Abstract Dedicated to the memory of Sir Michael Francis Atiyah (1929-2019) We give a characterization of Atiyah’s and Hitchin’s transverse Hilbert schemes of points on a symplectic surface in terms of bi-Poisson structures. Furthermore, we describe the geometry of hyperkähler manifolds arising from the transverse Hilbert scheme construction, with particular attention paid to the monopole moduli spaces.

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The O–C diagrams of minor planets − a new approach to modelling the rotation

International Astronomical Union Colloquium ◽

10.1017/s0252921100031407 ◽

1999 ◽

Vol 173 ◽

pp. 185-188

Author(s):

Gy. Szabó ◽

K. Sárneczky ◽

L.L. Kiss

Keyword(s):

Error Analysis ◽

Time Dependence ◽

Theoretical Work ◽

Minor Planet ◽

Minor Planets ◽

New Approach ◽

Preliminary Results ◽

Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

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