an:06607004
Zbl 1357.14061
Costa, Laura; Marchesi, Simone; Mir??-Roig, Rosa Maria
Tango bundles on Grassmannians
EN
Math. Nachr. 289, No. 8-9, 950-961 (2016).
00356767
2016
j
14M15 14F05
vector bundles; Grassmannians
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 \textit{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.
Luca Chiantini (Siena)
Zbl 1099.14045