Prehomogenous spaces and projective geometry
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منابع مشابه
Projective Geometry Lecture Notes
2 Vector Spaces and Projective Spaces 3 2.1 Vector spaces and their duals . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Projective spaces and homogeneous coordinates . . . . . . . . . . . . . . . 5 2.2.1 Visualizing projective space . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Homogeneous coordinates . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Linear subspaces . . . . ....
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Introduction 3 1. Affine geometry 4 1.1. Affine spaces 5 1.1.1. Euclidean geometry and its isometries 5 1.1.2. Affine spaces 7 1.1.3. Affine transformations 8 1.1.4. Tangent spaces 9 1.1.5. Acceleration and geodesics 10 1.1.6. Connections 11 1.2. The hierarchy of structures 11 1.3. Affine vector fields 12 1.4. Affine subspaces 13 1.5. Volume in affine geometry 14 1.6. Centers of gravity 14 1.7....
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We compute the representation zeta functions of some finitely generated nilpotent groups associated to unipotent group schemes over rings of integers in number fields. These group schemes are defined by Lie lattices whose presentations are modelled on certain prehomogeneous vector spaces. Our method is based on evaluating p-adic integrals associated to certain rank varieties of linear forms.
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The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in question fall into two separate classes, the negative or odd class that generalises quantum real projective planes and the positive or even class that genera...
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تاریخ انتشار 2012