Rings of automorphic forms which are not Cohen-Macaulay, II

Shigeaki TSUYUMINE

doi:10.2969/jmsj/04030369

Shigeaki TSUYUMINE

Author information

JOURNAL FREE ACCESS

1988 Volume 40 Issue 3 Pages 369-381

DOI https://doi.org/10.2969/jmsj/04030369

Details

Published: 1988 Received: September 05, 1986 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. Cartan, Fonctions automorphes, Ecole Normale Supérier Seminaire, 1957/58.
2) M. Eichler, Projective varieties and modular forms, Lecture Notes in Math., 210, Springer, 1970.
3) M. Eichler, On the graded ring of modular forms, Acta Arith., 18 (1971), 87-92.
4) E. Freitag, Lokale und globale Invarianten der Hilbertschen Modulgruppen, Invent. Math., 17 (1972), 106-134.
5) M. Eichler, Stabile Modulformen, Math. Ann., 230 (1977), 197-211.
6) M. Eichler, Die Irreducibilität der Schottky relation (Bemerkungen zu einem Satz von J. Igusa), Arch. Math., 40 (1983), 255-259.
7) E. Freitag und R. Kiehl, Algebraiche Eigenschaften der lokal Ringe in den Spitzen dear Hilbertschen Modulgruppen, Invent. Math., 24 (1974), 121-146.
8) H. Grauert und O. Riemenschneider, Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen, Invent. Math., 11 (1970), 263-292.
9) A. Grothendieck, Sur quelques points d'algèbre homologique, Tohoku Math. J., 9 (1957), 119-221.
10) A. Grothendieck, Éléments de géométrie algébrique, III, Publ. Math. IHES., 11 (1961).
11) R. Hartshorne, Residue and duality, Lecture Notes in Math., 20, Springer, 1966.
12) J. Igusa, On Siegel modular forms of genus two, Amer. J. Math., 84 (1962), 175-200; (II), Amer. J. Math., 86(1964), 392-412.
13) J. Igusa, Modular forms and projective invariants, Amer. J. Math., 89 (1967), 817-855.
14) J. Igusa, A desingularization problem in the theory of Siegel modular functions, Math. Ann., 168 (1967), 228-260.
15) S. Mori, On affine cones associated with polarized varieties, Japan. J. Math., 1 (1975), 301-309.
16) P. Samuel, On unique factorization domain, Illinois J. Math., 5 (1961), 1-17.
17) T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan, 24 (1972), 20-59.
18) S. Tsuyumine, Rings of modular forms (On Eichler's problem), Nagoya Math. J., 99 (1985), 31-44.
19) S. Tsuyumine, Rings of automorphic forms which are not Cohen-Macaulay, I, J. Math. Soc. Japan, 38 (1986), 147-162.
20) S. Tsuyumine, Factorial property of a ring of automorphic forms, Trans. Amer. Math. Soc., 296 (1986), 111-123.
21) S. Tsuyumine, On Siegel modular forms of degree three, Amer. J. Math., 108 (1986), 755-862; Addendum, Amer. J. Math., 1001-1003.
22) S. Tsuyumine, On the Siegel modular function field of degree three, Compositio Math., 63 (1987), 83-98.
23) K. Watanabe, Some remarks concerning Demazure's construction of normal graded rings, Nagoya Math. J., 83(1981), 203-211.

Right : [1] H. Cartan, Fonctions automorphes, Ecole Normale Supérier Seminaire, 1957/58.
[2] M. Eichler, Projective varieties and modular forms, Lecture Notes in Math., 210, Springer, 1970.
[3] M. Eichler, On the graded ring of modular forms, Acta Arith., 18 (1971), 87-92.
[4] E. Freitag, Lokale und globale Invarianten der Hilbertschen Modulgruppen, Invent. Math., 17 (1972), 106-134.
[5] M. Eichler, Stabile Modulformen, Math. Ann., 230 (1977), 197-211.
[6] M. Eichler, Die Irreducibilität der Schottky relation (Bemerkungen zu einem Satz von J. Igusa), Arch. Math., 40 (1983), 255-259.
[7] E. Freitag und R. Kiehl, Algebraiche Eigenschaften der lokal Ringe in den Spitzen dear Hilbertschen Modulgruppen, Invent. Math., 24 (1974), 121-146.
[8] H. Grauert und O. Riemenschneider, Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen, Invent. Math., 11 (1970), 263-292.
[9] A. Grothendieck, Sur quelques points d'algèbre homologique, Tôhoku Math. J., 9 (1957), 119-221.
[10] A. Grothendieck, Éléments de géométrie algébrique, III, Publ. Math. IHES., 11 (1961).
[11] R. Hartshorne, Residue and duality, Lecture Notes in Math., 20, Springer, 1966.
[12] J. Igusa, On Siegel modular forms of genus two, Amer. J. Math., 84 (1962), 175-200; (II), Amer. J. Math., 86 (1964), 392-412.
[13] J. Igusa, Modular forms and projective invariants, Amer. J. Math., 89 (1967), 817-855.
[14] J. Igusa, A desingularization problem in the theory of Siegel modular functions, Math. Ann., 168 (1967), 228-260.
[15] S. Mori, On affine cones associated with polarized varieties, Japan. J. Math., 1 (1975), 301-309.
[16] P. Samuel, On unique factorization domain, Illinois J. Math., 5 (1961), 1-17.
[17] T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan, 24 (1972), 20-59.
[18] S. Tsuyumine, Rings of modular forms (On Eichler's problem), Nagoya Math. J., 99 (1985), 31-44.
[19] S. Tsuyumine, Rings of automorphic forms which are not Cohen-Macaulay, I, J. Math. Soc. Japan, 38 (1986), 147-162.
[20] S. Tsuyumine, Factorial property of a ring of automorphic forms, Trans. Amer. Math. Soc., 296 (1986), 111-123.
[21] S. Tsuyumine, On Siegel modular forms of degree three, Amer. J. Math., 108 (1986), 755-862; Addendum, Amer. J. Math., 1001-1003.
[22] S. Tsuyumine, On the Siegel modular function field of degree three, Compositio Math., 63 (1987), 83-98.
[23] K. Watanabe, Some remarks concerning Demazure's construction of normal graded rings, Nagoya Math. J., 83(1981), 203-211.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!