A rank theorem for coherent analytic sheaves
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- by Günther Trautmann PDF
- Trans. Amer. Math. Soc. 157 (1971), 495-498 Request permission
Abstract:
Let $S$ be an analytic subvariety in ${C^n}$ and $\mathcal {F}$ a coherent analytic sheaf on ${C^n}$, such that $\mathcal {F}$ is locally free on ${C^n} - S$ and $\Gamma (U,\mathcal {F}) = \Gamma (U - S,\mathcal {F})$ for every open set $U \subset {C^n}$. It is shown that $\mathcal {F}$ is locally free everywhere, if $\text {codh} \mathcal {F} \geqq n - 1$ and $\dim S + \text {rank} \mathcal {F} \leqq n - 2$.References
- Maurice Auslander and David A. Buchsbaum, Codimension and multiplicity, Ann. of Math. (2) 68 (1958), 625–657. MR 99978, DOI 10.2307/1970159
- David A. Buchsbaum, A generalized Koszul complex. I, Trans. Amer. Math. Soc. 111 (1964), 183–196. MR 159859, DOI 10.1090/S0002-9947-1964-0159859-0
- J. A. Eagon and D. G. Northcott, Ideals defined by matrices and a certain complex associated with them, Proc. Roy. Soc. London Ser. A 269 (1962), 188–204. MR 142592, DOI 10.1098/rspa.1962.0170
- D. G. Northcott, Some remarks on the theory of ideals defined by matrices, Quart. J. Math. Oxford Ser. (2) 14 (1963), 193–204. MR 151482, DOI 10.1093/qmath/14.1.193
- Günter Scheja, Fortsetzungssätze der komplex-analytischen Cohomologie und ihre algebraische Charakterisierung, Math. Ann. 157 (1964), 75–94 (German). MR 176466, DOI 10.1007/BF01362668
- Günther Trautmann, Eine Bemerkung zur Struktur der kohärenten analytischen Garben, Arch. Math. (Basel) 19 (1968), 300–304 (German). MR 228709, DOI 10.1007/BF01899508
- G. Trautmann, Ein Endlichkeitssatz in der analytischen Geometrie, Invent. Math. 8 (1969), 143–174 (German). MR 251251, DOI 10.1007/BF01404617
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 157 (1971), 495-498
- MSC: Primary 32.50
- DOI: https://doi.org/10.1090/S0002-9947-1971-0276498-5
- MathSciNet review: 0276498