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We extend the work of A. Beauville on rank $2$ vector bundles on a smooth curve in several directions. We give families of examples with large dimension, add new existence and non-existence results and prove the existence of indecomposable limits with arbitrary rank. To construct the large dimensional families we use the examples of limits of rank $2$ trivial bundles on $\mathbb {P}^2$ and $\mathbb {P}^3$ due to C. Banica. We also consider a more flexible notion: limits of trivial bundles on nearby curves.
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참고문헌 (27)
참고문헌 신청
E. Arbarello / 2016 / Explicit Brill-Noether-Petri general curves / Comment. Math. Helv 91(3):477~491
E. Arbarello / 1981 / Footnotes to a paper of Beniamino Segre / Math. Ann 256(3):341~362
E. Arbarello / 2011 / Volume II, Grundlehren der Mathematischen Wissenschaften, 268 / Springer
M. Atiyah / 1956 / On the Krull-Schmidt theorem with application to sheaves / Bull. Soc. Math. France 84:307~317
M. Atiyah / 1957 / Vector bundles over an elliptic curve / Proc. London Math. Soc. 3(7):414~452
E. Arbarello / 1981 / Footnotes to a paper of Beniamino Segre / Math. Ann 256(3):341~362
E. Arbarello / 2011 / Volume II, Grundlehren der Mathematischen Wissenschaften, 268 / Springer
M. Atiyah / 1956 / On the Krull-Schmidt theorem with application to sheaves / Bull. Soc. Math. France 84:307~317
M. Atiyah / 1957 / Vector bundles over an elliptic curve / Proc. London Math. Soc. 3(7):414~452
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