Lower bounds for Betti numbers

Luchezar L. Avramov; Ragnar-Olaf Buchweitz

Compositio Mathematica (1993)

  • Volume: 86, Issue: 2, page 147-158
  • ISSN: 0010-437X

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Avramov, Luchezar L., and Buchweitz, Ragnar-Olaf. "Lower bounds for Betti numbers." Compositio Mathematica 86.2 (1993): 147-158. <http://eudml.org/doc/90214>.

@article{Avramov1993,
author = {Avramov, Luchezar L., Buchweitz, Ragnar-Olaf},
journal = {Compositio Mathematica},
keywords = {Hilbert series; multiplicity; graded algebra; Krull dimension},
language = {eng},
number = {2},
pages = {147-158},
publisher = {Kluwer Academic Publishers},
title = {Lower bounds for Betti numbers},
url = {http://eudml.org/doc/90214},
volume = {86},
year = {1993},
}

TY - JOUR
AU - Avramov, Luchezar L.
AU - Buchweitz, Ragnar-Olaf
TI - Lower bounds for Betti numbers
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 86
IS - 2
SP - 147
EP - 158
LA - eng
KW - Hilbert series; multiplicity; graded algebra; Krull dimension
UR - http://eudml.org/doc/90214
ER -

References

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  2. [B-E1] Buchsbaum, D. and Eisenbud, D., Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension 3, American Journal of Math.99 (1977), 447-485. Zbl0373.13006MR453723
  3. [B-E 2] Buchsbaum, D. and Eisenbud, D., Generic free resolutions and a family of generically perfect ideals, Adv. in Math.18 (1975), 245-301. Zbl0336.13007MR396528
  4. [Ch] Charalambous, H., Lower bounds for Betti numbers of multigraded modules, J. Algebra, 137 (1991), 491-500. Zbl0729.13014MR1094254
  5. [C-E] Charalambous, H. and Evans, E.G., Jr., Problems on Betti numbers of finite length modules, in Free Resolutions in Commutative Algebra and Algebraic Geometry, ed. by D. Eisenbud and C. Huneke, Res. Notes Math.2, Jones and Bartlett Publishers, Boston, (1992), 25-33. Zbl0767.13005MR1165315
  6. [C-E-M] Charalambous, H., Evans, E.G., Jr., and Miller, M., Betti numbers for modules of finite length, Proceedings Amer. Math. Soc.109 (1990), 63-70. Zbl0703.13014MR1013967
  7. [D-H-M] Dutta, S.P., Hochster, M. and McLaughlin, J.E., Modules of finite projective dimension with negative intersection multiplicities, Invent. Math.79 (1985), 253-291. Zbl0588.13020MR778127
  8. [E-N] Eagon, J.A. and Northcott, D.G., Ideals defined by matrices and a certain complex associated with them, Proc. Royal Soc., A, 269 (1962), 188-204. Zbl0106.25603MR142592
  9. [E-G 1] Evans, E.G., Jr. and Griffith, P., Syzygies, London Math. Soc. Lecture Note Series 106, Cambridge Univ. Press (1985). Zbl0569.13005MR811636
  10. [E-G2] Evans, E.G., Jr. and Griffith, P., Binomial behaviour of Betti numbers for modules of finite length, Pacific J. Math.133 (1988), 267-276. Zbl0653.13009MR941922
  11. [Ha] Hartshorne, R., Algebraic vector bundles on projective spaces: a problem list, Topology18 (1979), 117-128. Zbl0417.14011MR544153
  12. [Ko] Kobayashi, Y., On the multiplicity of graded algebras, Math. Japonica24 (1980), 643-655. Zbl0434.13009MR565552
  13. [P-S] Peskine, C. and Szpiro, L., Syzygies et multiplicités, C.R.A.S. Sér. A-B278 (1974), 1421-1424. Zbl0281.13004MR349659
  14. [Ro] Roberts, P., Intersection Theorems, in Commutative Algebra, ed. by M. Hochster, C. Huneke, J. D. Sally; MSRI Publications 15, Springer Verlag, New York, (1989), 417-437. Zbl0734.13009MR1015532
  15. [Sa] Santoni, L., Horrocks' question for monomially graded modules, Pacific J. Math.141 (1990), 105-124. Zbl0692.13009MR1028267
  16. [Sm] Smoke, W., Dimension and multiplicity for graded algebras, J. Algebra21 (1972), 149-173. Zbl0231.13006MR309920

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