Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We present a method to construct non-singular cubic surfaces over ℚ with a Galois invariant double-six. We start with cubic surfaces in the hexahedral form of L. Cremona and Th. Reye. For these, we develop an explicit version of Galois descent.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
646-661
Opis fizyczny
Daty
wydano
2010-08-01
online
2010-07-24
Twórcy
- Mathematisches Institut, Universität Bayreuth, Bayreuth, Germany, Stephan.Elsenhans@uni-bayreuth.de
autor
- Fachbereich 6 Mathematik, Siegen, Germany, jahnel@mathematik.uni-siegen.de
Bibliografia
- [1] Bourbaki N., Éléments de Mathématique, Livre II: Algèbre, Chapitre V, Masson, Paris, 1981
- [2] Coble A.B., Point sets and allied Cremona groups I, Trans. Amer. Math. Soc., 1915, 16(2), 155–198
- [3] Cremona L., Ueber die Polar-Hexaeder bei den Flächen dritter Ordnung, Math. Ann., 1878, 13(2), 301–304 http://dx.doi.org/10.1007/BF01446536[Crossref]
- [4] Dolgachev I.V., Topics in classical algebraic geometry. Part I, preprint available at http://www.math.lsa.umich.edu/˜idolga/topics1.pdf
- [5] Ekedahl T., An effective version of Hilbert’s irreducibility theorem, In: Séminaire de Théorie des Nombres (1988–1989 Paris), Progr. Math., 91, Birkhäuser, Boston, 1990, 241–249
- [6] Elsenhans A.-S., Good models for cubic surfaces, preprint available at http://www.staff.uni-bayreuth.de/˜btm216/red_5.pdf
- [7] Elsenhans A.-S., Jahnel J., Experiments with general cubic surfaces, In: Algebra, Arithmetic and Geometry - Manin Festschrift, (in press), preprint available at http://www.math.nyu.edu/˜tschinke/.manin/submitted/jahnel.pdf
- [8] Elsenhans A.-S., Jahnel J., The discriminant of a cubic surface, preprint available at http://www.uni-math.gwdg.de/jahnel/Preprints/Oktik7.ps
- [9] Glauberman G., On the Suzuki groups and the outer automorphisms of S 6, In: Groups, difference sets, and the Monster (1993 Columbus/Ohio), de Gruyter, Berlin, 1996, 55–72
- [10] Hartshorne R., Algebraic Geometry, Graduate Texts in Mathematics, 52, Springer, New York-Heidelberg, 1977
- [11] Malle G., Matzat B.H., Inverse Galois Theory, Springer, Berlin, 1999
- [12] Manin Y.I., Cubic Forms: Algebra, Geometry, Arithmetic, Elsevier, New York, 1974
- [13] Reye T., Über Polfünfecke und Polsechsecke räumlicher Polarsysteme, J. Reine Angew. Math., 1874, 77, 269–288
- [14] Schläfli L., An attempt to determine the twenty-seven lines upon a surface of the third order, and to divide such surfaces into species in reference to the reality of the lines upon the surface, Quart. J. Math., 1858, 2, 110–120
- [15] Schläfli L., Quand’è che dalla superficie generale di terzo ordine si stacca una parte che non sia realmente segata da ogni piano reale?, Ann. Math. Pura Appl., 1872, 5, 289–295 [Crossref]
- [16] Serre J.-P., Groupes Algébriques et Corps de Classes, Publications de l’Institut de Mathématique de l’Université de Nancago, VII, Hermann, Paris, 1959
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0036-1