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Tango bundles on Grassmannians. (English) Zbl 1357.14061
The authors construct examples of indecomposable vector bundles on Grassmannians \(\mathrm{Gr}(r,k)\), whose rank is smaller than the dimension of \(\mathrm{Gr}(r,k)\). These bundles are obtained as a quotient of globally generated bundles, by generalizing the construction of H. Tango for rank \(n-1\) bundles on \(\mathbb P^n\). The proof of the existence is based on computations in Schubert calculus, which are performed by means of a method introduced by L. Gatto [Asian J. Math. 9, No. 3, 315–322 (2005; Zbl 1099.14045)]. The authors describe the structure of Tango bundles on Grassmannians and prove that they are stable (in the sense of Mumford-Takemoto). Finally, the authors describe the component of Tango bundles in the Maruyama moduli scheme.
MSC:
14M15 Grassmannians, Schubert varieties, flag manifolds
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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