An approach to the characteristic free Dutta multiplicity

Kazuhiko KURANO

doi:10.2969/jmsj/04530369

Kazuhiko KURANO

著者情報

ジャーナルフリー

1993 年 45 巻 3 号 p. 369-390

DOI https://doi.org/10.2969/jmsj/04530369

詳細

Published: 1993 Received: 1991/04/30 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
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) D. A. Buchsbaum and D. Eisenbud, What makes a complex exact?, J. Algebra, 25 (1973), 259-268.
2) D. A. Buchsbaum and D. Eisenbud, Algebra structures for finite free resolutions and some structure theorem for ideals of codimension 3, Amer. J. Math., 99 (1977), 447-485.
3) D. A. Buchsbaum and D. S. Rim, A generalized Koszul complex II. Depth and multiplicity, Trans. Amer. Math. Soc., 3 (1964), 197-225.
4) S. P. Dutta, Frobenius and multiplicities, J. Algebra, 85 (1983), 424-448.
5) S. P. Dutta, A special case of positivity, Proc. Amer. Math. Soc., 103 (1988), 344-346.
6) S. P. Dutta, M. Hochster and J. E. MacLaughlin, Modules of finite projective dimension with negative intersection multiplicities, Invent. Math., 79 (1985), 253-291.
7) E. G. Evans and P. Griffith, Syzygies, London Math. Soc. Lecture Note Ser., 106, Cambridge Univ. Press, Cambridge, 1985.
8) W. Fulton, Intersection Theory, Springer, 1984.
9) H. Gillet and C. Soulé, K-théorie et nullité des multiplicities d'intersection, C. R. Acad. Sci. Paris Ser. I Math., 300 (1985), 71-74.
10) A. Grothendieck, Local Cohomology, Lecture Notes in Math., 41, Springer, 1967.
11) A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique IV, Publ. Math. IHES, Ibid., 20 (1964), 24 (1965), 28 (1966), 32 (1967).
12) H. Kleppe and D. Laksov, The algebra structure and deformation of pfaffian schemes, J. Algebra, 64 (1980), 167-189.
13) K. Kurano, Relations on pfaffians I: plethysm formulas, J. Math. Kyoto Univ., 31 (1991), 713-731.
14) M. Nagata, Local Rings, Interscience Tracts in Pure and Appl. Math., Wiley, New York, 1962.
15) P. Roberts, The vanishing of intersection multiplicities and perfect complexes, Bull. Amer. Math. Soc., 13 (1985), 127-130.
16) P. Roberts, MacRae invariant and the first local chern character, Trans. Amer. Math. Soc., 300 (1987), 583-591.
17) P. Roberts, Local Chern characters and intersection multiplicities, Proc. Sympos. Pure Math., 46 (1987), 389-400.
18) P. Roberts, Intersection theorems, Commutative algebra, Proc. Microprogram, June 15-July 12, 1987, Math. Sci. Res. Inst. Publ., 15, Springer, 1989, pp. 417-436.
19) P. Roberts, Local Chern classes, multiplicities, and perfect complexes, Société Mathématique de France Mémoire, 38 (1989), 145-161.
20) J.-P. Serre, Algèbra locale. Multiplicités, Lecture Notes in Math., 11, Springer, 1965.
21) G. Seibert, Complexes with homology of finite length and Frobenius functions, J. Algebra, 125 (1989), 278-287.

Right : [1] D. A. Buchsbaum and D. Eisenbud, What makes a complex exact?, J. Algebra, 25 (1973), 259-268.
[2] D. A. Buchsbaum and D. Eisenbud, Algebra structures for finite free resolutions and some structure theorem for ideals of codimension 3, Amer. J. Math., 99 (1977), 447-485.
[3] D. A. Buchsbaum and D. S. Rim, A generalized Koszul complex II. Depth and multiplicity, Trans. Amer. Math. Soc., 3 (1964), 197-225.
[4] S. P. Dutta, Frobenius and multiplicities, J. Algebra, 85 (1983), 424-448.
[5] S. P. Dutta, A special case of positivity, Proc. Amer. Math. Soc., 103 (1988), 344-346.
[6] S. P. Dutta, M. Hochster and J. E. MacLaughlin, Modules of finite projective dimension with negative intersection multiplicities, Invent. Math., 79 (1985), 253-291.
[7] E. G. Evans and P. Griffith, Syzygies, London Math. Soc. Lecture Note Ser., 106, Cambridge Univ. Press, Cambridge, 1985.
[8] W. Fulton, Intersection Theory, Springer, 1984.
[9] H. Gillet and C. Soulé, K-théorie et nullité des multiplicities d'intersection, C. R. Acad. Sci. Paris Ser. I Math., 300 (1985), 71-74.
[10] A. Grothendieck, Local Cohomology, Lecture Notes in Math., 41, Springer, 1967.
[11] A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique IV, Publ. Math. IHES, Ibid., 20 (1964), 24 (1965), 28 (1966), 32 (1967).
[12] H. Kleppe and D. Laksov, The algebra structure and deformation of pfaffian schemes, J. Algebra, 64 (1980), 167-189.
[13] K. Kurano, Relations on pfaffians I: plethysm formulas, J. Math. Kyoto Univ., 31 (1991), 713-731.
[14] M. Nagata, Local Rings, Interscience Tracts in Pure and Appl. Math., Wiley, New York, 1962.
[15] P. Roberts, The vanishing of intersection multiplicities and perfect complexes, Bull. Amer. Math. Soc., 13 (1985), 127-130.
[16] P. Roberts, MacRae invariant and the first local chern character, Trans. Amer. Math. Soc., 300 (1987), 583-591.
[17] P. Roberts, Local Chern characters and intersection multiplicities, Proc. Sympos. Pure Math., 46 (1987), 389-400.
[18] P. Roberts, Intersection theorems, Commutative algebra, Proc. Microprogram, June 15-July 12, 1987, Math. Sci. Res. Inst. Publ., 15, Springer, 1989, pp. 417-436.
[19] P. Roberts, Local Chern classes, multiplicities, and perfect complexes, Société Mathématique de France Mémoire, 38 (1989), 145-161.
[20] J. -P. Serre, Algèbra locale. Multiplicités, Lecture Notes in Math., 11, Springer, 1965.
[21] G. Seibert, Complexes with homology of finite length and Frobenius functions, J. Algebra, 125 (1989), 278-287.

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