Costa, Laura; Marchesi, Simone; Miró-Roig, Rosa Maria Tango bundles on Grassmannians. (English) Zbl 1357.14061 Math. Nachr. 289, No. 8-9, 950-961 (2016). 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. Reviewer: Luca Chiantini (Siena) MSC: 14M15 Grassmannians, Schubert varieties, flag manifolds 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) Keywords:vector bundles; Grassmannians PDF BibTeX XML Cite \textit{L. Costa} et al., Math. Nachr. 289, No. 8--9, 950--961 (2016; Zbl 1357.14061) Full Text: DOI References: [1] Cascini, Weighted Tango bundles on Pn and their moduli spaces, Forum Math. 13 (2) pp 251– (2001) · Zbl 1009.14003 · doi:10.1515/form.2001.007 [2] Cordovez, Newton Binomial Formulas in Schubert Calculus, Rev. Mat. Complut. 22 (1) pp 129– (2009) · Zbl 1168.14038 · doi:10.5209/rev_REMA.2009.v22.n1.16330 [3] Fulton, Intersection Theory (1998) · doi:10.1007/978-1-4612-1700-8 [4] Gatto, Schubert Calculus via Hasse-Schmidt Derivations, Asian J. Math. 9 (3) pp 295– (2005) · Zbl 1099.14045 · doi:10.4310/AJM.2005.v9.n3.a2 [5] Griffiths, Principles of Algebraic Geometry (1994) · doi:10.1002/9781118032527 [6] Hoppe, Generischer spaltungstyp und zweite Chernklasse stabiler Vektorraumbndel vom rang 4 auf 4, Math. Z. 187 (1984) · Zbl 0567.14011 · doi:10.1007/BF01161952 [7] Jaczewski, On the geometry of Tango bundles, Teubner-Texte Math. 92 pp 177– (1986) [8] Ottaviani, A class of n-bundles on Gr(k,n), J. Reine Angew. Math. 379 pp 182– (1987) · Zbl 0611.14015 [9] Tango, An example of indecomposable vector bundle of rank n-1 on Pn, J. Math. Kyoto Univ. 16 pp 137– (1976) · Zbl 0339.14008 · doi:10.1215/kjm/1250522965 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.