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Home > Mathematics and Science Textbooks > Mathematics > Geometry > Algebraic geometry > Ruled Varieties: An Introduction to Algebraic Differential Geometry(Advanced Lectures in Mathematics)
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Ruled Varieties: An Introduction to Algebraic Differential Geometry(Advanced Lectures in Mathematics)

Ruled Varieties: An Introduction to Algebraic Differential Geometry(Advanced Lectures in Mathematics)


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About the Book

Gegenstand des Buches ist der Zusammenhang zwischen globaler algebraischer Geometrie, projektiver Varietäten und lokaler Differentialgeometrie. Es beschäftigt sich genauer mit sogenannten "Geregelten Varietäten", die Vereinigung von linearen Räumen sind. Das Buch ist entstanden aus Vorlesungen des ersten Autors für Studenten im Hauptstudium mit Grundkenntnissen in algebraischer Geometrie und führt an den Rand aktueller Forschung. Das Thema ist klassisch und heute wieder aktuell geworden. Die Grundlagen, die in der Literatur nur schwer zu finden sind, werden hier sorgfältig aufgeschrieben und mit elementaren Methoden zugänglich gemacht. Die neueren Ergebnisse aus der Forschung sind im letzten Kapitel dargestellt. Das Buch eignet sich z. B. gut für ein Seminar oder eine Vorlesung für Studierende, deren Schwerpunkt "Algebraische Geometrie" ist.

Table of Contents:
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.

About the Author :
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.


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Product Details
  • ISBN-13: 9783528031381
  • Publisher: Springer Fachmedien Wiesbaden
  • Publisher Imprint: Vieweg+Teubner Verlag
  • Height: 240 mm
  • No of Pages: 142
  • Returnable: N
  • Sub Title: An Introduction to Algebraic Differential Geometry
  • ISBN-10: 3528031387
  • Publisher Date: 29 May 2001
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: Advanced Lectures in Mathematics
  • Width: 170 mm


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Ruled Varieties: An Introduction to Algebraic Differential Geometry(Advanced Lectures in Mathematics)
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