Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Nonstable reflexive sheaves on $ {\bf P}\sp{3}$


Author: Timothy Sauer
Journal: Trans. Amer. Math. Soc. 281 (1984), 633-655
MSC: Primary 14F05; Secondary 14M10
DOI: https://doi.org/10.1090/S0002-9947-1984-0722766-9
MathSciNet review: 722766
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The spectrum is defined for nonstable rank two reflexive sheaves on $ {{\mathbf{P}}^3}$ and is used to establish vanishing theorems for intermediate cohomology in terms of the Chern classes and the order of nonstability. These results are shown to be best possible and the extremal cases are classified. Some applications to Cohen-Macaulay generically local complete intersection curves in $ {{\mathbf{P}}^3}$ are given.


References [Enhancements On Off] (What's this?)

  • [1] W. Barth and G. Elencwajg, Concernant la cohomologie des fibrés algébriques stables sur $ {{\mathbf{P}}_n}({\mathbf{C}})$, Lecture Notes in Math., vol. 683, Springer, Berlin and New York, 1978, pp. 1-24. MR 517517 (80f:14004)
  • [2] L. Ein, R. Hartshorne and H. Vogelaar, Restriction theorems for stable rank $ 3$ vector bundles on $ {{\mathbf{P}}^n}$, Math. Ann. 259 (1982), 541-569. MR 660047 (84b:14006)
  • [3] D. Ferrand, Construction de fibrés de rang $ 2$, C. R. Acad. Sci. Paris Sér. A 281 (1975), 345-347. MR 0379517 (52:422)
  • [4] H. Grauert and M. Schneider, Komplexe Unterräume und holomorphe Vektorraumbündel vom Rang zwei, Math. Ann. 230 (1977), 75-90. MR 0481134 (58:1279)
  • [5] R. Hartshorne, Stable reflexive sheaves, Math. Ann. 254 (1980), 121-176. MR 597077 (82b:14011)
  • [6] -, Stable reflexive sheaves. II, Invent. Math. 66 (1982), 165-190. MR 652652 (83e:14012)
  • [7] -, Stable vector bundles of rank $ 2$ on $ {{\mathbf{P}}^3}$, Math. Ann. 238 (1978), 229-280. MR 514430 (80c:14011)
  • [8] C. Peskine and L. Szpiro, Liaison des variétés algébriques. I, Invent. Math. 26 (1974), 271-302. MR 0364271 (51:526)
  • [9] A. P. Rao, Liaison among curves in $ {{\mathbf{P}}^3}$, Invent. Math. 50 (1979), 205-217. MR 520926 (80e:14023)
  • [10] R. L. E. Schwarzenberger, Vector bundles on the projective plane, Proc. London Math. Soc. (3) 11 (1961), 623-640. MR 0137712 (25:1161)
  • [11] F. Takemoto, Stable vector bundles on algebraic surfaces, Nagoya Math. J. 47 (1972). MR 0337966 (49:2735)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 14F05, 14M10

Retrieve articles in all journals with MSC: 14F05, 14M10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0722766-9
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society