Premium
Tango bundles on Grassmannians
Author(s) -
Costa Laura,
Marchesi Simone,
MiróRoig Rosa Maria
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500015
Subject(s) - vector bundle , mathematics , indecomposable module , grassmannian , rank (graph theory) , pure mathematics , variety (cybernetics) , bundle , fiber bundle , combinatorics , statistics , materials science , composite material
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 ofP 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.