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Symplectic Resolution
In mathematics, particularly in representation theory, a symplectic resolution is a morphism that combines symplectic geometry and resolution of singularities. Definition Let \pi: Y \to X be a morphism between complex algebraic varieties, where Y is Smooth algebraic variety, smooth and carries a symplectic structure, and X is affine variety, affine, normal variety, normal, and carries a Poisson structure. Then \pi is a ''symplectic resolution'' if and only if \pi is projective morphism, projective, birational, and Poisson. A conical symplectic resolution is one that is equipped with compatible group action, actions of \mathbb^\times on both X and Y. Under these actions, X contracts to a single point (denoted 0), the symplectic form is scaled with weight 2, and the morphism \pi is compatible with these actions. The ''core'' of a conical symplectic resolution is defined as the central fibre (mathematics), fiber F_0 = \pi^(0). A conical symplectic resolution is Hamiltonian if it pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
