scholarly journals The tropical momentum map: a classification of toric log symplectic manifolds

2016 ◽  
Vol 367 (3-4) ◽  
pp. 1217-1258 ◽  
Author(s):  
Marco Gualtieri ◽  
Songhao Li ◽  
Álvaro Pelayo ◽  
Tudor S. Ratiu
Keyword(s):  
Symplectic Manifolds ◽  
Momentum Map

scholarly journals Classification of Equivariant Star Products on Symplectic Manifolds

2016 ◽  
Vol 106 (5) ◽  
pp. 675-692 ◽  
Author(s):  
Thorsten Reichert ◽  
Stefan Waldmann
Keyword(s):  
Symplectic Manifolds ◽  
Star Products

The complete classification of generalized homogeneous symplectic manifolds

1989 ◽  
Vol 30 (11) ◽  
pp. 2476-2483 ◽  
Author(s):  
D. R. Grigore ◽  
O. T. Popp
Keyword(s):  
Complete Classification ◽  
Symplectic Manifolds

scholarly journals Classification of six-dimensional monotone symplectic manifolds admitting semifree circle actions I

2019 ◽  
Vol 30 (06) ◽  
pp. 1950032 ◽  
Author(s):  
Yunhyung Cho
Keyword(s):  
Symplectic Manifold ◽  
Symplectic Manifolds ◽  
Complete List ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Circle Actions ◽  
Isolated Point

Let [Formula: see text] be a six-dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian [Formula: see text]-action. We show that if the minimal (or maximal) fixed component of the action is an isolated point, then [Formula: see text] is [Formula: see text]-equivariantly symplectomorphic to some Kähler Fano manifold [Formula: see text] with a certain holomorphic [Formula: see text]-action. We also give a complete list of all such Fano manifolds and describe all semifree [Formula: see text]-actions on them specifically.

scholarly journals Using angular momentum maps to detect kinematically distinct galactic components

2020 ◽  
Vol 501 (2) ◽  
pp. 2182-2197
Author(s):  
Dimitrios Irodotou ◽  
Peter A Thomas
Keyword(s):  
Spatial Distribution ◽  
Angular Momentum ◽  
Surface Density ◽  
Grid Cell ◽  
Angular Separation ◽  
Morphological Classification ◽  
Density Profiles ◽  
Momentum Map ◽  
Rotating Discs

ABSTRACT In this work, we introduce a physically motivated method of performing disc/spheroid decomposition of simulated galaxies, which we apply to the eagle sample. We make use of the healpix package to create Mollweide projections of the angular momentum map of each galaxy’s stellar particles. A number of features arise on the angular momentum space which allows us to decompose galaxies and classify them into different morphological types. We assign stellar particles with angular separation of less/greater than 30° from the densest grid cell on the angular momentum sphere to the disc/spheroid components, respectively. We analyse the spatial distribution for a subsample of galaxies and show that the surface density profiles of the disc and spheroid closely follow an exponential and a Sérsic profile, respectively. In addition discs rotate faster, have smaller velocity dispersions, are younger and are more metal rich than spheroids. Thus, our morphological classification reproduces the observed properties of such systems. Finally, we demonstrate that our method is able to identify a significant population of galaxies with counter-rotating discs and provide a more realistic classification of such systems compared to previous methods.

scholarly journals Classification of Invariant Star Products up to Equivariant Morita Equivalence on Symplectic Manifolds

2011 ◽  
Vol 100 (2) ◽  
pp. 203-236 ◽  
Author(s):  
Stefan Jansen ◽  
Nikolai Neumaier ◽  
Gregor Schaumann ◽  
Stefan Waldmann
Keyword(s):  
Symplectic Manifolds ◽  
Morita Equivalence ◽  
Star Products

scholarly journals Elliptic singularities on log symplectic manifolds and Feigin–Odesskii Poisson brackets

2017 ◽  
Vol 153 (4) ◽  
pp. 717-744 ◽  
Author(s):  
Brent Pym
Keyword(s):  
Symplectic Form ◽  
Symplectic Structure ◽  
Transversality Condition ◽  
Symplectic Manifolds ◽  
Poisson Brackets ◽  
Poisson Structures ◽  
Elliptic Point ◽  
Surface Singularities ◽  
Complex Symplectic

A log symplectic manifold is a complex manifold equipped with a complex symplectic form that has simple poles on a hypersurface. The possible singularities of such a hypersurface are heavily constrained. We introduce the notion of an elliptic point of a log symplectic structure, which is a singular point at which a natural transversality condition involving the modular vector field is satisfied, and we prove a local normal form for such points that involves the simple elliptic surface singularities$\widetilde{E}_{6},\widetilde{E}_{7}$and$\widetilde{E}_{8}$. Our main application is to the classification of Poisson brackets on Fano fourfolds. For example, we show that Feigin and Odesskii’s Poisson structures of type$q_{5,1}$are the only log symplectic structures on projective four-space whose singular points are all elliptic.

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