A geometric construction of Tango bundle on P^5
Abstract
The Tango bundle T over P^5 is proved to be the pull-back of the twisted Cayley bundle C(1) via a map f : P^5 --> Q_5 existing only in characteristic 2. The Frobenius morphism F factorizes via such f. Using f the cohomology of T is computed in terms of F^*(C), Sym^2(C), C and the tensor product of S by C, while these are computed by applying Borel-Bott-Weil theorem. By machine-aided computation the mimimal resolutions of C and T are given; incidentally the matrix presenting the spinor bundle S over Q_5 is shown.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- November 2001
- DOI:
- 10.48550/arXiv.math/0111207
- arXiv:
- arXiv:math/0111207
- Bibcode:
- 2001math.....11207F
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14F05 (Primary);
- 14-04;
- 14J60 (Secondary)
- E-Print:
- 9 pages, no figures, ams-latex