an:05762956
Zbl 1200.14085
Farnik, ??ucja; Frapporti, Davide; Marchesi, Simone
On the non-existence of orthogonal instanton bundles on \(\mathbb P^{2n+1}\)
EN
Matematiche 64, No. 2, 81-90 (2009).
00265295
2009
j
14J60
instanton bundles
Instanton bundles are vector bundles \(E\) of rank \(2n\), on a projective space of odd dimension \(2n+1\), arising as the middle cohomology of a monad. There are examples of instanton bundles which are symplectic, in the sense that there exists an isomorphism \(\alpha: E\to E^*\) such that \(\alpha = -\alpha^*\). In particular, every instanton bundle on \(\mathbb P^3\) is symplectic. One could rise the question about the existence of orthogonal instanton bundles, i.e. bundles endowed with an isomorphism \(\alpha\) as above, with \(\alpha =\alpha^*\). The authors close the question, by showing that no instanton bundles are orthogonal.
Luca Chiantini (Siena)