Del i serien Advanced Lectures in Mathematics

Ruled Varieties

An Introduction to Algebraic Differential Geometry

Häftad, Engelska, 2001

AvGerd Fischer,Jens Piontkowski,Gerd Fischer,Jens Piontkowski

549 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

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.

Produktinformation

Utgivningsdatum2001-05-29
Mått170 x 240 x 9 mm
Vikt278 g
FormatHäftad
SpråkEngelska
SerieAdvanced Lectures in Mathematics
Antal sidor142
FörlagSpringer Fachmedien Wiesbaden
ISBN9783528031381

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik

Prof. Dr. em. Gerd Fischer war viele Jahre Professor fur Mathematik an der Universitat Dusseldorf. Er ist jetzt Gastprofessor an der Fakultat fur Mathematik der TU Munchen. Gerd Fischer ist Autor zahlreicher erfolgreicher Lehrbucher, u.a. der Linearen Algebra (vieweg studium - Grundkurs Mathematik). Dr. Jens Piontkowski ist Hochschuldozent am Mathematischen Institut der Heinrich-Heine-Universitat Dusseldorf.

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.

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Del i serien Advanced Lectures in Mathematics

Ruled Varieties

An Introduction to Algebraic Differential Geometry

Häftad, Engelska, 2001

AvGerd Fischer,Jens Piontkowski,Gerd Fischer,Jens Piontkowski

549 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Produktinformation

Utgivningsdatum2001-05-29
Mått170 x 240 x 9 mm
Vikt278 g
FormatHäftad
SpråkEngelska
SerieAdvanced Lectures in Mathematics
Antal sidor142
FörlagSpringer Fachmedien Wiesbaden
ISBN9783528031381

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik

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.