Rings of automorphic forms which are not Cohen-Macaulay, I
ジャーナル
フリー
1986 年 38 巻 1 号 p. 147-162
詳細
- Published: 1986 Received: 1984/06/26 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
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訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報 訂正内容: Wrong : 1) A. Ash, D. Mumford, M. Rapoport and Y.-S. Tai, Smooth compactification of locally symmetric varieties, Math. Sci. Press, Brookline, Massachusetts, 1975.
2) W. L. Baily and A. Borel, Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math., 84 (1966), 442-528.
3) H. Cartan, Fonctions automorphes, École Norm. Sup., Séminaire Henri Cartan 1957/1958, Secrétariat mathématique, Paris.
4) M. Eichler, Projective varieties and modular forms, Lecture Notes in Math., 210, Springer-Verlag, 1971.
5) M. Eichler, On the graded rings of modular forms, Acta Arith., 18 (1971), 87-92.
6) E. Freitag, Lokale and globale Invarianten der Hilbertschen Modulgruppen, Invent. Math., 17 (1972), 106-134.
7) E. Freitag, Stabile Modulformen, Math. Ann., 230 (1977), 197-211.
8) E. Freitag, Die Irreducibilität der Schottky relation (Bemerkungen zu einem Satz von Igusa), Archiv der Math., 40(1983), 255-259.
9) E. Freitag and R. Kiehl, Algebraische Eigenschaf ten der lokal Ringe in der Hilbertschen Modulgruppen, Invent. Math., 24 (1974), 121-146.
10) E. Gottschling, Über die Fixpunkte der Siegelschen Modulgruppen, Math. Ann., 143 (1961), 111-149.
11) H. Grauert and O. Riemenschneider, Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen, Invent. Math., 11 (1970), 263-292.
12) A. Grothendieck, Éléments de géométrie algébrique, III, Publ. Math. I. H. E. S., 11, 1961.
13) A. Grothendieck, Sur quelques points d'algèbre homologique, Tohoku Math. J., 9 (1957), 119-221.
14) R. Hartshorne, Algebraic geometry, Graduate Texts in Math., 52, Springer-Verlag, 1977.
15) M. Hochster and J. A. Eagon, Cohen-Macaulay rings, invariant theory and the generic perfection of determinantal loci, Amer. J. Math., 93 (1971), 1020-1058.
16) J. Igusa, On Siegel modular forms of genus two, (II), Amer. J. Math., 86 (1964), 392-412.
17) J. Igusa, On the theory of compactifications, Summer Institute on Algebraic Geometry, Woods Hole, Amer. Math. Soc., 1964, (mimeographed).
18) D. Mumford, Hirzebruch's proportionality theorem in the noncompact case, Invent. Math., 42 (1977), 239-272.
19) J. Lipman, Unique factorization in complete local rings, in Algebraic Geometry-Arcata 1974, Proc. Symposia in Pure Math., 29, Amer. Math. Soc., 531-546.
20) H. L. Resnikoff and Y.-S. Tai, On the structure of a graded ring of automorphic forms on the 2-dimensional complex ball, Math. Ann., 238 (1978), 97-117.
21) O. Riemenschneider, Characterizing Moišezon space by almost positive coherent sheaves, Math. Z., 123 (1971), 263-284.
22) P. Samuel, On unique factorization domains, Illinois J. Math., 5 (1961), 1-17.
23) J.-P. Serre, Prolongement de faisceaux analytiques cohérent, Ann. Inst. Fourier (Grenoble), 16 (1966), 363-374.
24) R. Stanley, Invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc. (New series), 1 (1979), 475-511.
25) Y.-S. Tai, On the Kodaira dimension of the moduli space of abelian varieties, Invent. Math., 68 (1982), 425-439.
26) Y.-S. Tai and H. L. Resnikoff, On the structure of a graded ring of automorphic forms on the 2-dimensional complex ball, II, Math. Ann., 258 (1982), 367-382.
27) S. Tsuyumine, Rings of modular forms (On Eichler's problem), Nagoya Math. J., 99 (1985), 31-44.
28) S. Tsuyumine, Rings of automorphic forms which are not Cohen-Macaulay, II, (in preparation).
Right : [1] A. Ash, D. Mumford, M. Rapoport and Y. -S. Tai, Smooth compactification of locally symmetric varieties, Math. Sci. Press, Brookline, Massachusetts, 1975.
[2] W. L. Baily and A. Borel, Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math., 84 (1966), 442-528.
[3] H. Cartan, Fonctions automorphes, École Norm. Sup., Séminaire Henri Cartan 1957/1958, Secrétariat mathématique, Paris.
[4] M. Eichler, Projective varieties and modular forms, Lecture Notes in Math., 210, Springer-Verlag, 1971.
[5] M. Eichler, On the graded rings of modular forms, Acta Arith., 18 (1971), 87-92.
[6] E. Freitag, Lokale und globale Invarianten der Hilbertschen Modulgruppen, Invent. Math., 17 (1972), 106-134.
[7] E. Freitag, Stabile Modulformen, Math. Ann., 230 (1977), 197-211.
[8] E. Freitag, Die Irreducibilität der Schottky relation (Bemerkungen zu einem Satz von Igusa), Archiv der Math., 40 (1983), 255-259.
[9] E. Freitag and R. Kiehl, Algebraische Eigenschaften der lokal Ringe in der Hilbertschen Modulgruppen, Invent. Math., 24 (1974), 121-146.
[10] E. Gottschling, Über die Fixpunkte der Siegelschen Modulgruppen, Math. Ann., 143 (1961), 111-149.
[11] H. Grauert and O. Riemenschneider, Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen, Invent. Math., 11 (1970), 263-292.
[12] A. Grothendieck, Éléments de géométrie algébrique, III, Publ. Math. I. H. E. S., 11, 1961.
[13] A. Grothendieck, Sur quelques points d'algèbre homologique, Tôhoku Math. J., 9 (1957), 119-221.
[14] R. Hartshorne, Algebraic geometry, Graduate Texts in Math., 52, Springer-Verlag, 1977.
[15] M. Hochster and J. A. Eagon, Cohen-Macaulay rings, invariant theory and the generic perfection of determinantal loci, Amer. J. Math., 93 (1971), 1020-1058.
[16] J. Igusa, On Siegel modular forms of genus two, (II), Amer. J. Math., 86 (1964), 392-412.
[17] J. Igusa, On the theory of compactifications, Summer Institute on Algebraic Geometry, Woods Hole, Amer. Math. Soc., 1964, (mimeographed).
[18] D. Mumford, Hirzebruch's proportionality theorem in the noncompact case, Invent. Math., 42 (1977), 239-272.
[19] J. Lipman, Unique factorization in complete local rings, in Algebraic Geometry-Arcata 1974, Proc. Symposia in Pure Math., 29, Amer. Math. Soc., 531-546.
[20] H. L. Resnikoff and Y. -S. Tai, On the structure of a graded ring of automorphic forms on the 2-dimensional complex ball, Math. Ann., 238 (1978), 97-117.
[21] O. Riemenschneider, Characterizing Moišezon space by almost positive coherent sheaves, Math. Z., 123 (1971), 263-284.
[22] P. Samuel, On unique factorization domains, Illinois J. Math., 5 (1961), 1-17.
[23] J. -P. Serre, Prolongement de faisceaux analytiques cohérent, Ann. Inst. Fourier (Grenoble), 16 (1966), 363-374.
[24] R. Stanley, Invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc. (New series), 1 (1979), 475-511.
[25] Y. -S. Tai, On the Kodaira dimension of the moduli space of abelian varieties, Invent. Math., 68 (1982), 425-439.
[26] Y. -S. Tai and H. L. Resnikoff, On the structure of a graded ring of automorphic forms on the 2-dimensional complex ball, II, Math. Ann., 258 (1982), 367-382.
[27] S. Tsuyumine, Rings of modular forms (On Eichler's problem), Nagoya Math. J., 99 (1985), 31-44.
[28] S. Tsuyumine, Rings of automorphic forms which are not Cohen-Macaulay, II, (in preparation).
訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル 訂正内容: -
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