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A geometric construction of Tango bundle on \(\mathbb{P}^5\). (English) Zbl 1093.14506

Summary: The Tango bundle \(T\) over \(\mathbb{P}^5\) [H. Tango, J. Math. Kyoto Univ. 16, 201–207 (1976; Zbl 0326.14015)] is proved to be the pull–back of the twisted Cayley bundle \(C(1)\) via a map \(f \colon \mathbb{P}^5 \rightarrow Q_5\) existing only in characteristic 2. The Frobenius morphism \(\varphi\) factorizes via such \(f\).

MSC:

14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli

Citations:

Zbl 0326.14015
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