Splitting criterion for reflexive sheaves

Splitting criterion for reflexive sheaves
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by Takuro Abe and Masahiko Yoshinaga PDF

Proc. Amer. Math. Soc. 136 (2008), 1887-1891 Request permission

We give a criterion for a reflexive sheaf to split into a direct sum of line bundles.

References

Robin Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics, Vol. 156, Springer-Verlag, Berlin-New York, 1970. Notes written in collaboration with C. Musili. MR 0282977, DOI 10.1007/BFb0067839
Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157, DOI 10.1007/978-1-4757-3849-0
Robin Hartshorne, Stable reflexive sheaves, Math. Ann. 254 (1980), no. 2, 121–176. MR 597077, DOI 10.1007/BF01467074
Hideyuki Matsumura, Commutative algebra, W. A. Benjamin, Inc., New York, 1970. MR 0266911
Christian Okonek, Michael Schneider, and Heinz Spindler, Vector bundles on complex projective spaces, Progress in Mathematics, vol. 3, Birkhäuser, Boston, Mass., 1980. MR 561910
Peter Orlik and Hiroaki Terao, Arrangements of hyperplanes, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 300, Springer-Verlag, Berlin, 1992. MR 1217488, DOI 10.1007/978-3-662-02772-1
Hiroaki Terao, Free arrangements of hyperplanes and unitary reflection groups, Proc. Japan Acad. Ser. A Math. Sci. 56 (1980), no. 8, 389–392. MR 596011
Masahiko Yoshinaga, Characterization of a free arrangement and conjecture of Edelman and Reiner, Invent. Math. 157 (2004), no. 2, 449–454. MR 2077250, DOI 10.1007/s00222-004-0359-2