×

zbMATH — the first resource for mathematics

On the collineation group of a normal projective Abelian variety. (English) Zbl 0337.14029
MSC:
14K10 Algebraic moduli of abelian varieties, classification
14K25 Theta functions and abelian varieties
14H10 Families, moduli of curves (algebraic)
11F27 Theta series; Weil representation; theta correspondences
PDF BibTeX XML Cite
Full Text: Numdam EuDML
References:
[1] Andreotti , Sopra le varietà di Picard d’una superficie algebrica , Rend. Accad. Lincei , vol. X , May 1951 , pp. 380 - 85 . Zbl 0049.11101 · Zbl 0049.11101
[2] Andreotti , Recherches sur les surfaces algébriques irregulières , Mém. Acad. Roy. Belgique , 27 ( 1952 ), pp. 1 - 36 . MR 58248 | Zbl 0048.37902 · Zbl 0048.37902
[3] Andreotti-Mayer , On period relations for Abelian integrals on algebraic curves , Annali Scuola Normale Superiore di Pisa , vol. XXI , fasc. II ( 1967 ). Numdam | Zbl 0222.14024 · Zbl 0222.14024
[4] Appell , Sur les fonctions périodiques de deux variables , J. de Math. , serie IV , 7 ( 1891 ), pp. 157 - 219 . Article | JFM 23.0430.01 · JFM 23.0430.01
[5] 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 . JFM 39.0698.03 · JFM 39.0698.03
[6] Bianchi , Funzioni ellittiche , Zanichelli, Bologna , 1930 .
[7] H. Cartan , Fonctions thêta sur le tore, I, II, Sem. H. Cartan , 1951-52 .
[8] Cartier , Quantum mechanical commutation relations and theta functions , Proceedings of Symposia in Pure Mathematics, vol. IX , 1966 . MR 216825 | Zbl 0178.28401 · Zbl 0178.28401
[9] Chow , On compact complex analytic varieties , American Journal of Math. , 71 ( 1949 ), pp. 893 - 914 . MR 33093 | Zbl 0041.48302 · Zbl 0041.48302
[10] Chow , , Van der Waerden , , Zag , , IX, Über zugeordnete Formen und algebraische Systeme von algebraischen Mannigfaltigkeiten , Math. Annalen , 113 ( 1937 ), pp. 692 - 704 . Zbl 0016.04004 | JFM 62.0772.02 · Zbl 0016.04004
[11] Conforto , Abelsche Funktionen und algebraische Geometrie , Springer , Band 84 , Berlin , 1956 . MR 79316 | Zbl 0074.36601 · Zbl 0074.36601
[12] Courant - Hurwitz , Funktionentheorie, Grundlehren Math. Wiss ., Band 3 , 4 Auflage , Berlin , 1964 .
[13] Dolbeault , Fonctions theta associées à un diviseur donné , H. Cartan’s Séminaire , 1952 . Numdam
[14] Enriques - Severi , Mémoire sur les surfaces hyperelliptiques , Acta Mathematica , 32 ( 1909 ), pp. 283 - 392 and 33 ( 1910 ), pp. 321 - 399 . JFM 41.0522.01 · JFM 41.0522.01
[15] Farkas , On the Schottky relation and its generalization to arbitrary genus , Annals. of Mathematics , July 1970 , pp. 57 - 81 . MR 264057 | Zbl 0202.07902 · Zbl 0202.07902
[16] Farkas - Rauch , Period relations of Schottky type on Riemann surfaces , Annals of Mathematics , 1970 . Zbl 0204.09602 · Zbl 0204.09602
[17] Frobenius Über die Grundlagen der Theorie der Jacobischen Funktionen, J.f.r.u. angewandte Math . (Crelle, J.), 17 ( 1884 ), pp. 16 - 48 , 188 - 223 . JFM 16.0378.01 · JFM 16.0378.01
[18] Hodge - Pedoe , Methods of algebraic Geometry, I, II , Cambridge Un. Press , 1952 . · Zbl 0048.14502
[19] Humbert , Théorie générale des surfaces hyperelliptiques , J. Math . (IV), 9 ( 1893 ), pp. 29 - 170 and 361 - 475 . Article | JFM 25.1220.01 · JFM 25.1220.01
[20] 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 . Article | MR 1510374 | JFM 19.0472.01 · JFM 19.0472.01
[21] Igusa , On the Picard varieties attached to algebraic varieties , American Journal of Mathematics , 74 ( 1952 ), pp. 1 - 22 . MR 46076 | Zbl 0049.38601 · Zbl 0049.38601
[22] Igusa , Theta functions, Grundlehren Bd., 194 , Springer , New York , 1972 . MR 325625 | Zbl 0251.14016 · Zbl 0251.14016
[23] 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 . JFM 40.0489.03 · JFM 40.0489.03
[24] 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 .
[25] Kloosterman , The behaviour of general theta functions under the modular group , Ann. of Math. , 47 ( 1946 ), pp. 317 - 45 . Zbl 0063.03262 · Zbl 0063.03262
[26] Krazer Lehrbuch der Thetafunktionen , Chelsea, N.Y. , 1970 (reprint of the 1903 original edition). Zbl 0212.42901 · Zbl 0212.42901
[27] Krazer-Prym , Neue Grundlagen einer Theorie der allgemeinen Thetafunctionen , B. G. Teubner , Leipzig , 1892 . JFM 23.0492.02 · JFM 23.0492.02
[28] Krazer - Wirtinger , Abelsche Functionen und allgemeine Thetafunktionen , Enz. der Math. Wiss. II , B . 7 , S. 636 . JFM 47.0362.04 · JFM 47.0362.04
[29] Lang , Abelian varieties , Interscience Pub. Inc. , New York , 1959 . MR 106225 | Zbl 0098.13201 · Zbl 0098.13201
[30] 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 . MR 1501178 | JFM 48.0428.03 · JFM 48.0428.03
[31] Morikawa , On Abelian varieties , Nagoya Math. Journal , 6 ( 1953 ), pp. 151 - 170 . Article | MR 59025 | Zbl 0052.38001 · Zbl 0052.38001
[32] D. Mumford , Abelian varieties , Oxford University Press , 1970 . MR 282985 | Zbl 0223.14022 · Zbl 0223.14022
[33] 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 . MR 204427 | Zbl 0219.14024 · Zbl 0219.14024
[34] H. Poincaré , Sur les propriétés du potentiel et sur les fonctions abeliennes , Acta Mathematica , 22 ( 1899 ), pp. 89 - 178 . JFM 29.0370.02 · JFM 29.0370.02
[35] Rosati , Sopra le funzioni abeliani pari e le varietà abeliane di rango due , Rendiconti di Matematica, Appl. , Roma ( 1952 ), pp. 28 - 61 . Zbl 0048.14701 · Zbl 0048.14701
[36] 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 . MR 61416 | Zbl 0049.38602 · Zbl 0049.38602
[37] Samuel , Méthodes d’Algèbre abstraite en Géométrie algébrique , 2 -nd Ed., Ergebrisse der Math. , Bd. 4 , Springer , 1967 . Zbl 0146.16901 · Zbl 0146.16901
[38] 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 . MR 424698 | Zbl 0217.43301 · Zbl 0217.43301
[39] Schottky , Über die Moduln der Thetafunctionen , Acta Math. , 1903 , pp. 235 - 288 . JFM 34.0506.03 · JFM 34.0506.03
[40] Schottky , Zur Theorie der Abelscher Funktionen von vier Variabeln , J. Reine Ang. Math ., 102 ( 1888 ), pp. 304 - 352 . Article | JFM 20.0488.02 · JFM 20.0488.02
[41] C.L. Siegel , Analytic functions of several complex variables , Lectures at the Institute ofr Advanced Study , 1948-49 . MR 34847 | Zbl 0036.05004 · Zbl 0036.05004
[42] 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 . MR 166196 | Zbl 0122.32102 · Zbl 0122.32102
[43] Traynard , Sur les fonctions thêta de deux variables et les surfaces hyperelliptiques , Annales de l’Ecole normale supérieure , S. II , 24 ( 1907 ), Cap. VIII. Numdam | JFM 38.0481.01 · JFM 38.0481.01
[44] Van Der Waerden , Einführung in die Algebraische Geometrie , Springer , Berlin , 1939 . Zbl 0021.25001 | JFM 65.1393.01 · Zbl 0021.25001
[45] A. Weil , Théorèmes fondamentaux de la théorie des fonctions thêta, Séminaire Bourbake, Exp . 16 , 1949 . Numdam | Zbl 0111.27603 · Zbl 0111.27603
[46] A. Weil , Variétés Kähleriennes , Act. Sci. Ind . 1267 , Hermann , Paris , 1958 .. MR 111056
[47] A. Weil , Lecture notes on algebraic fibre bundles , Chicago .
[48] A. Weil , On the projective embedding of Abelian varieties, Algebraic Geom. and Topology (Symposium in Honor of Lefschetz) , Princeton Un. Press , 1957 . MR 84850 | Zbl 0091.33301 · Zbl 0091.33301
[49] A. Weil , Foundations of algebraic Geometry , Colloquium AMS , vol. XXIX , 2 -nd Ed., 1962 . MR 144898 | Zbl 0168.18701 · Zbl 0168.18701
[50] Wirtinger , Untersuchungen über Thetafunktionen , B. G. Teubner , Leipzig , 1815 . JFM 26.0514.01 · JFM 26.0514.01
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.