27 Geraden

Literatur

Cayley - Salmon: Briefwechsel
Jakob Steiner: Crelle's Journal für Mathematik 53 (133-141),
Siehe auch: Steiner's Werke II, 651-659.
Jordan: Oevres I, p.199-202, 203-206, 249-268)
Felix Klein: Vorlesungen über die Entwicklung der Mathematik im 19.Jahrhundert. p.166-167
David Hilbert, Stefan Cohn-Vossen: Anschauliche Geometrie.
- Die Schläfli'sche Doppelsechs (§ 25. p.146-151)
- Die 27 Geraden (p.145-146, 149-151)
A. Henderson: The 27 lines upon the cubic surface, Cambridge, University Press, 1911.

Yu. Manin: Cubic Forms. Algebra, Geometry, Arithmetic.. Second Edition. North Holland 1986.
Chapter VI. The Twenty-Seven Lines.
Gottfired Barthel, Friedrich Hirzebruch, Thomas Höfer: Geradenkonfigurationen und Algebraische Flächen. Vieweg 1987.

Van der Waerden: Einführung in die algebraische Geometrie Springer Verlag 1939 (und 1973), 148-153.
David Mumford: Algebraic Geometry I.
Er schreibt in der Einleitung: My goal is precisely to convey some of the classical geometric ideas and to get "off the ground": in fact, to get to the 27 lines on the cubic - surely one of the gems hidden in the rag-bad of projective geometry.
M. Reid: Undergraduate Algebraic Geometry. LMS Student Texts 12 Cambridge University Press 1988.
Klaus Hulek: Elementare algebraische Geometrie. (Vieweg studium, 2000).
Ausschnitt.
Phillip Griffith and Joseph Harris: Principles of Algebraic Geometry. Wylie 1978. p.480-489
Gezeigt wird zum Beispiel: Jede glatte kubische Fläche entsteht aus der prjektiven Ebene durch Aufblasen von 6 Punkten (Beweis: pp.486-489)
Robin Hartshorne: Algebraic Geometry. Springer 1977. pp.395-406.
I.R.Shafarevich. Basic Algebraic Geometry. Springer 1974.

Oliver Labs, The Cubic Surface Homepage (früher: Algebraic Geometry Group, University of Mainz, Germany).
Siehe auch Geraden auf Flächen
Surfer

Das Literaturverzeichnis der Arbeit von Yamashita: An elementary and purely synthetic proof for the double six theorem of Schläfli.

Harvard (Angela Vierling-Claassen)

http://www.ph-heidelberg.de/wp/filler/3dcg.html
http://www.ph-heidelberg.de/wp/filler/

Nigel Hitchin (Oxford University, UK): E6, E7, E8. Presentation (at the Clay Institute, as part of the 2005 Academy Colloquium Series)
Abstract. These three symbols represent to a modern mathematician three Dynkin diagrams, but in a sense they have been known to mathematicians for hundreds of years. When the Greeks classified the regular solids, they were really showing they knew about E6, E7 and E8 and when the 19th century geometers got excited about the 27 lines on a cubic surface or the 28 bitangents to a quartic curve they were really studying E6 and E7 in their own terms. Today string theorists search for a theory of the universe by looking at E8 X E8. The talk will aim to show how E6, E7 and E8 lie at the heart of some very concrete mathematics.

Last modified: Tue Sep 15 13:41:18 CET 2008