On the collineation group of a normal projective abelian variety
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1975)
- Volume: 2, Issue: 1, page 45-87
- ISSN: 0391-173X
Access Full Article
topHow to cite
topGaeta, Federico. "On the collineation group of a normal projective abelian variety." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 2.1 (1975): 45-87. <http://eudml.org/doc/83685>.
@article{Gaeta1975,
author = {Gaeta, Federico},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {45-87},
publisher = {Scuola normale superiore},
title = {On the collineation group of a normal projective abelian variety},
url = {http://eudml.org/doc/83685},
volume = {2},
year = {1975},
}
TY - JOUR
AU - Gaeta, Federico
TI - On the collineation group of a normal projective abelian variety
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1975
PB - Scuola normale superiore
VL - 2
IS - 1
SP - 45
EP - 87
LA - eng
UR - http://eudml.org/doc/83685
ER -
References
top- [1] Andreotti, Sopra le varietà di Picard d'una superficie algebrica, Rend. Accad. Lincei, vol. X, May 1951, pp. 380-85. Zbl0049.11101
- [2] Andreotti, Recherches sur les surfaces algébriques irregulières, Mém. Acad. Roy. Belgique, 27 (1952), pp. 1-36. Zbl0048.37902MR58248
- Andreotti-Mayer, On period relations for Abelian integrals on algebraic curves, Annali Scuola Normale Superiore di Pisa, vol. XXI, fasc. II (1967). Zbl0222.14024
- Appell, Sur les fonctions périodiques de deux variables, J. de Math., serie IV, 7 (1891), pp. 157-219. Zbl23.0430.01JFM23.0430.01
- Bagnera-De Franchis, Le superficie algebriche le quali ammettono una rappresentazione parametrica mediante funzioni iperellittiche di due argomenti, Memoria della Società dei XL, serie III, 15 (1908), pp. 251-343. Zbl39.0698.03JFM39.0698.03
- Bianchi, Funzioni ellittiche, Zanichelli, Bologna, 1930.
- H. Cartan, Fonctions thêta sur le tore, I, II, Sem. H. Cartan, 1951-52.
- Cartier, Quantum mechanical commutation relations and theta functions, Proceedings of Symposia in Pure Mathematics, vol. IX, 1966. Zbl0178.28401MR216825
- Chow, On compact complex analytic varieties, American Journal of Math., 71 (1949), pp. 893-914. Zbl0041.48302MR33093
- Chow, , Van der Waerden, , Zag, , IX, Über zugeordnete Formen und algebraische Systeme von algebraischen Mannigfaltigkeiten, Math. Annalen, 113 (1937), pp. 692-704. Zbl0016.04004JFM62.0772.02
- Conforto, AbelscheFunktionen und algebraische Geometrie, Springer, Band 84, Berlin, 1956. Zbl0074.36601MR79316
- Courant - Hurwitz, Funktionentheorie, Grundlehren Math. Wiss., Band 3, 4Auflage, Berlin, 1964.
- Dolbeault, Fonctions theta associées à un diviseur donné, H. Cartan's Séminaire, 1952.
- Enriques - Severi, Mémoire sur les surfaces hyperelliptiques, Acta Mathematica, 32 (1909), pp. 283-392 and 33 (1910), pp. 321-399. Zbl40.0684.01JFM41.0522.01
- Farkas, On the Schottky relation and its generalization to arbitrary genus, Annals. of Mathematics, July 1970, pp. 57-81. Zbl0202.07902MR264057
- Farkas - Rauch, Period relations of Schottky type on Riemann surfaces, Annals of Mathematics, 1970. Zbl0204.09602
- FrobeniusÜber die Grundlagen der Theorie der Jacobischen Funktionen, J.f.r.u. angewandte Math. (Crelle, J.), 17 (1884), pp. 16-48, 188-223. JFM16.0378.01
- Hodge - Pedoe, Methods of algebraic Geometry, I, II, CambridgeUn. Press, 1952. Zbl0048.14502
- Humbert, Théorie générale des surfaces hyperelliptiques, J. Math. (IV), 9 (1893), pp. 29-170 and 361-475. Zbl25.1220.01JFM25.1220.01
- Hurwitz, Über endliche Gruppe linearer Substitutionen, welche in der Theorie der elliptischen Transzendenten auftreten, Mathematische Annalen, Bd. 27 (1886), pp. 183-233; Mathematische Werke, Bd. I, Funktionentheorie, p. 189. MR1510374JFM19.0472.01
- [1] Igusa, On the Picard varieties attached to algebraic varieties, American Journal of Mathematics, 74 (1952), pp. 1-22. Zbl0049.38601MR46076
- [2] Igusa, Theta functions, Grundlehren Bd., 194, Springer, New York, 1972. Zbl0251.14016MR325625
- Jung - Schottky, Neue Sätze über Symmetralfunktionen und die Abelschen Funktionen der Riemannscher Theorie, Sitzungsberichte der Preussischen Acad. Wiss. (Berlin) Phys. Math. Classe (1909), pp. 282-297. Zbl40.0489.03JFM40.0489.03
- Klein, Über die elliptischen Normalkurven der n-ten Ordnung, Abh. math. phys. Klasse der Sachsischen Kgl. Gesellschaft der Wiss., Bd. 13, Nr. IV(1885) or Gesammelte Mathematische Abhandlungen, III, Berlin, Springer, 1923, pp. 198-254.
- Kloosterman, The behaviour of general theta functions under the modular group, Ann. of Math., 47 (1946), pp. 317-45. Zbl0063.03262
- KrazerLehrbuch der Thetafunktionen, Chelsea, N.Y., 1970 (reprint of the 1903 original edition). Zbl0212.42901
- Krazer-Prym, Neue Grundlagen einer Theorie der allgemeinen Thetafunctionen, B. G. Teubner, Leipzig, 1892. JFM23.0492.02
- Krazer - Wirtinger, Abelsche Functionen und allgemeine Thetafunktionen, Enz. der Math. Wiss. II, B. 7, S. 636. Zbl47.0362.04JFM47.0362.04
- Lang, Abelian varieties, Interscience Pub. Inc., New York, 1959. Zbl0098.13201MR106225
- Lefschetz, On certain numerical invariants of algebraic varieties with application to Abelian varieties, Trans. Amer. Math. Soc., 22 (1921), pp. 327-482, reprinted in Selected Papers, Chelsea, N. Y., 1971. Zbl48.0428.03MR1501178JFM48.0428.03
- Morikawa, OnAbelian varieties, Nagoya Math. Journal, 6 (1953), pp. 151-170. Zbl0052.38001MR59025
- [1] D. Mumford, Abelian varieties, Oxford University Press, 1970. Zbl0223.14022MR282985
- [2] D. Mumford, On the equations defining Abelian varieties, I-III, Invent. Math., 1 (1966), pp. 287-354; 3 (1967), pp. 75-135 and 215-244. Zbl0219.14024MR204427
- H. Poincaré, Sur les propriétés du potentiel et sur les fonctions abeliennes, Acta Mathematica, 22 (1899), pp. 89-178. JFM29.0370.02
- [1] Rosati, Sopra le funzioni abeliani pari e le varietà abeliane di rango due, Rendiconti di Matematica, Appl., Roma (1952), pp. 28-61. Zbl0048.14701
- [2] Rosati, Osservazioni su alcuni gruppi, finiti di omografie appartenenti ad una varietà di Picard e ad una varietà abeliana di rango due, Rendiconti di Matematica, Appl. Roma (1952), pp. 453-469. Zbl0049.38602MR61416
- Samuel, Méthodes d'Algèbre abstraite en Géométrie algébrique, 2-nd Ed., Ergebrisse der Math., Bd. 4, Springer, 1967. Zbl0146.16901
- Satake, Fock representations and theta-functions, Advances in the Theory of Riemann surfaces, Proceedings of the 1969 Stony Brook Conference, Annals of Mathematics Studies, Princeton Un. Press, 1971. Zbl0217.43301MR424698
- [1] Schottky, Über die Moduln der Thetafunctionen, Acta Math., 1903, pp. 235-288. Zbl34.0506.03JFM34.0506.03
- [2] Schottky, Zur Theorie der Abelscher Funktionen von vier Variabeln, J. Reine Ang. Math., 102 (1888), pp. 304-352. JFM20.0488.02
- [1] C.L. Siegel, Analytic functions of several complex variables, Lectures at the Institute ofr Advanced Study, 1948-49. Zbl0036.05004MR34847
- [2] C.L. Siegel, Moduln Abelscher Funktionen, Nachrichten der Akad. Wiss. Gyttingen, Math.-Phys. Klasse 1960, N. 25, pp. 365-427 and Gesammelte Abhandlungeu, vol. III, Springer, Berlin, 1966. Zbl0122.32102MR166196
- Traynard, Sur les fonctions thêta de deux variables et les surfaces hyperelliptiques, Annales de l'Ecole normale supérieure, S. II, 24 (1907), Cap. VIII. Zbl38.0481.01JFM38.0481.01
- Van Der Waerden, Einführung in die Algebraische Geometrie, Springer, Berlin, 1939. Zbl0021.25001JFM65.1393.01
- [1] A. Weil, Théorèmes fondamentaux de la théorie des fonctions thêta, Séminaire Bourbake, Exp. 16, 1949. Zbl0111.27603
- [2] A. Weil, Variétés Kähleriennes, Act. Sci. Ind. 1267, Hermann, Paris, 1958.. MR111056
- [3] A. Weil, Lecture notes on algebraic fibre bundles, Chicago.
- [4] A. Weil, On the projective embedding of Abelian varieties, Algebraic Geom. and Topology (Symposium in Honor of Lefschetz), Princeton Un. Press, 1957. Zbl0091.33301MR84850
- [5] A. Weil, Foundations of algebraic Geometry, Colloquium AMS, vol. XXIX, 2-nd Ed., 1962. Zbl0168.18701MR144898
- Wirtinger, Untersuchungen über Thetafunktionen, B. G. Teubner, Leipzig, 1815. JFM26.0514.01
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.