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On the non-existence of orthogonal instanton bundles on $$\mathbb P^{2n+1}$$. (English) Zbl 1200.14085
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.

##### MSC:
 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
##### Keywords:
instanton bundles
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