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Weakly uniform rank two vector bundles on multiprojective spaces. (English) Zbl 1229.14016
The authors classify weakly uniform rank two vector bundles on multiprojective spaces and give a criterion for rank 2 vector bundle \(E\) to be weakly uniform and also the condition for vector bundle \(E\) to split. They also show that every rank \(r>2\) weakly uniform vector bundle with splitting type \(a_{1,1} = \dots = a_{r,s}=0\) is trivial and every rank \(r>2\) uniform vector bundle with splitting type \(a_1 > \dots > a_r\) splits.
MSC:
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
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[1] DOI: 10.2969/jmsj/02810123 · Zbl 0315.14003
[2] DOI: 10.1007/978-3-0348-0151-5 · Zbl 1237.14003
[3] DOI: 10.1017/S0305004100037920
[4] Ellia, Mém. Soc. Math. Fr. 7 pp 59– (1982)
[5] Elencwajg, Vector Bundles and Differential Equations (Proc. Conf., Nice, 1979) pp 37– (1980)
[6] DOI: 10.1017/S0305004100036410
[7] Drezet, C. R. Acad. Sci. Paris Sér. A 291 pp 125– (1980)
[8] DOI: 10.1112/jlms/s2-31.2.211 · Zbl 0535.14009
[9] Ballico, Bull. Soc. Math. France 111 pp 59– (1983)
[10] Van de Ven, Math. Ann. 195 pp 245– (1972) · Zbl 0215.43202
[11] DOI: 10.1007/BF01420242 · Zbl 0378.14003
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