Tango bundles on Grassmannians. Issue 8 (10th November 2015)

• Record Type: Journal Article
• Authors: Costa, Laura; Marchesi, Simone; Miró‐Roig, Rosa Maria
• Is Part Of: Mathematische Nachrichten. Volume 289:Issue 8/9(2016)
• Page Start: 950
• Page End: 961
• Publication Date: 2015-11-10
• Subjects: Tango bundles -- Grassmannians -- Primary: 14F05 -- 14M15; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201500015
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : The goal of this paper is to prove the existence of indecomposable rank ( ( k + 1 ) ( n − k ) − ( k + 1 ) ) vector bundles on the Grassmannian variety Gr ( k, n ) . We will call them Tango bundles since in the particular case of P n ≅ Gr ( 0, n ) they correspond to the celebrated vector bundle discovered by H. Tango in 1974. We will give a geometrical description of Tango bundles and we will prove that they are μ‐stable.