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Produktbild: Ruled Varieties

Ruled Varieties An Introduction to Algebraic Differential Geometry

Aus der Reihe Advanced Lectures in Mathematics

36,99 €

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

29.05.2001

Verlag

Vieweg & Teubner

Seitenzahl

142

Maße (L/B/H)

24/17/0,8 cm

Gewicht

278 g

Auflage

Softcover reprint of the original 1st ed. 2001

Sprache

Englisch

ISBN

978-3-528-03138-1

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

29.05.2001

Verlag

Vieweg & Teubner

Seitenzahl

142

Maße (L/B/H)

24/17/0,8 cm

Gewicht

278 g

Auflage

Softcover reprint of the original 1st ed. 2001

Sprache

Englisch

ISBN

978-3-528-03138-1

Herstelleradresse

Vieweg+Teubner Verlag
Abraham-Lincoln-Straße 46
65189 Wiesbaden
DE

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  • Produktbild: Ruled Varieties
  • 0 Review from Classical Differential and Projective Geometry.- 0.1 Developable Rulings.- 0.2 Vanishing Gauß Curvature.- 0.3 Hessian Matrices.- 0.4 Classification of Developable Surfaces in ?3.- 0.5 Developable Surfaces in ?3(?).- 1 Grassmannians.- 1.1 Preliminaries.- 1.1.1 Algebraic Varieties.- 1.1.2 Rational Maps.- 1.1.3 Holomorphic Linear Combinations.- 1.1.4 Limit Direction of a Holomorphic Path.- 1.1.5 Radial Paths.- 1.2 Plücker Coordinates.- 1.2.1 Local Coordinates.- 1.2.2 The Plücker Embedding.- 1.2.3 Lines in ?3.- 1.2.4 The Plücker Image.- 1.2.5 Plücker Relations.- 1.2.6 Systems of Vector Valued Functions.- 1.3 Incidences and Duality.- 1.3.1 Equations and Generators in Terms of Plücker Coordinates.- 1.3.2 Flag Varieties.- 1.3.3 Duality of Grassmannians.- 1.3.4 Dual Projective Spaces.- 1.4 Tangents to Grassmannians.- 1.4.1 Tangents to Projective Space.- 1.4.2 The Tangent Space of the Grassmannian.- 1.5 Curves in Grassmannians.- 1.5.1 The Drill.- 1.5.2 Derived Curves.- 1.5.3 Sums and Intersections.- 1.5.4 Associated Curves and Curves with Prescribed Drill.- 1.5.5 Normal Form.- 2 Ruled Varieties.- 2.1 Incidence Varieties and Duality.- 2.1.1 Unions of Linear Varieties.- 2.1.2 Fano Varieties.- 2.1.3 Joins.- 2.1.4 Conormal Bundle and Dual Variety.- 2.1.5 Duality Theorem.- 2.1.6 The Contact Locus.- 2.1.7 The Dual Curve.- 2.1.8 Rational Curves.- 2.2 Developable Varieties.- 2.2.1 Rulings.- 2.2.2 Adapted Parameterizations.- 2.2.3 Germs of Rulings.- 2.2.4 Developable Rulings and Focal Points.- 2.2.5 Developability of Joins.- 2.2.6 Dual Varieties of Cones and Degenerate Varieties.- 2.2.7 Tangent and Osculating Scrolls.- 2.2.8 Classification of Developable One Parameter Rulings.- 2.2.9 Example of a “Twisted Plane”.- 2.2.10 Characterization of Drill One Curves.- 2.3 The Gauß Map.- 2.3.1 Definition of the Gauß Map.- 2.3.2 Linearity of the Fibers.- 2.3.3 Gauß Map and Developability.- 2.3.4 Gauß Image and Dual Variety.- 2.3.5 Existence of Varieties with Given Gauß Rank.- 2.4 The Second Fundamental Form.- 2.4.1 Definition of the Second Fundamental Form.- 2.4.2 The Degeneracy Space.- 2.4.3 The Degeneracy Map.- 2.4.4 The Singular and Base Locus.- 2.4.5 The Codimension of a Uniruled Variety.- 2.4.6 Fibers of the Gauß Map.- 2.4.7 Characterization of Gauß Images.- 2.4.8 Singularities of the Gauß Map.- 2.5 Gauß Defect and Dual Defect.- 2.5.1 Dual Defect of Segre Varieties.- 2.5.2 Gauß Defect and Singular Locus.- 2.5.3 Dual Defect and Singular Locus.- 2.5.4 Computation of the Dual Defect.- 2.5.5 The Surface Case.- 2.5.6 Classification of Developable Hypersurfaces.- 2.5.7 Dual Defect of Uniruled Varieties.- 2.5.8 Varieties with Very Small Dual Varieties.- 3 Tangent and Secant Varieties.- 3.1 Zak’s Theorems.- 3.1.1 Tangent Spaces, Tangent Cones, and Tangent Stars.- 3.1.2 Zak’s Theorem on Tangent and Secant Varieties.- 3.1.3 Theorem on Tangencies.- 3.2 Third and Higher Fundamental Forms.- 3.2.1 Definition.- 3.2.2 Vanishing of Fundamental Forms.- 3.3 Tangent Varieties.- 3.3.1 The Dimension of the Tangent Variety.- 3.3.2 Developability of the Tangent Variety.- 3.3.3 Singularities of the Tangent Variety.- 3.4 The Dimension of the Secant Variety.- List of Symbols.