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＜電子ブック＞
Ruled Varieties : An Introduction to Algebraic Differential Geometry / by Gerd Fischer, Jens Piontkowski
(Advanced Lectures in Mathematics. ISSN:25127039)

版	1st ed. 2001.
出版者	Wiesbaden : Vieweg+Teubner Verlag : Imprint: Vieweg+Teubner Verlag
出版年	2001
本文言語	英語
大きさ	X, 142 p : online resource
冊子体	Ruled varieties : an introduction to algebraic differential geometry / Gerd Fischer, Jens Piontkowski
著者標目	*Fischer, Gerd author Piontkowski, Jens author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Probabilities LCSH:Geometry FREE:Algebraic Geometry FREE:Probability Theory FREE:Geometry
一般注記	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 -- 1.2 Plücker Coordinates -- 1.3 Incidences and Duality -- 1.4 Tangents to Grassmannians -- 1.5 Curves in Grassmannians -- 2 Ruled Varieties -- 2.1 Incidence Varieties and Duality -- 2.2 Developable Varieties -- 2.3 The Gauß Map -- 2.4 The Second Fundamental Form -- 2.5 Gauß Defect and Dual Defect -- 3 Tangent and Secant Varieties -- 3.1 Zak’s Theorems -- 3.2 Third and Higher Fundamental Forms -- 3.3 Tangent Varieties -- 3.4 The Dimension of the Secant Variety -- List of Symbols Ruled varieties are unions of a family of linear spaces. They are objects of algebraic geometry as well as differential geometry, especially if the ruling is developable. This book is an introduction to both aspects, the algebraic and differential one. Starting from very elementary facts, the necessary techniques are developed, especially concerning Grassmannians and fundamental forms in a version suitable for complex projective algebraic geometry. Finally, this leads to recent results on the classification of developable ruled varieties and facts about tangent and secant varieties. Compared to many other topics of algebraic geometry, this is an area easily accessible to a graduate course Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-322-80217-0

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