Cohomology of Tango bundle on $\mathbb{P}^5$
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 319-326.

Voir la notice de l'article dans Biblioteca Digitale Italiana di Matematica

-- Il fibrato di Tango è definito come pull-back del fibrato di Cayley $C$ su una e quadrica liscia $Q_5$ in $\mathbb{P}_6$ attraverso una funzione $f$ definita in caratteristica 2 che fattorizza il morfismo di Frobenius $\varphi$. La coomologia di $T$ è calcolata in termini di $S \otimes C$, $\varphi^*(C)$, $\text{Sym}^2(C)$ e $C$, che si studiano con il teorema di Borel-Bott-Weil. 
@article{BUMI_2006_8_9B_2_a5,
     author = {Faenzi, Daniele},
     title = {Cohomology of {Tango} bundle on $\mathbb{P}^5$},
     journal = {Bollettino della Unione matematica italiana},
     pages = {319--326},
     publisher = {mathdoc},
     volume = {Ser. 8, 9B},
     number = {2},
     year = {2006},
     zbl = {1178.14011},
     mrnumber = {2233141},
     language = {it},
     url = {https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_2_a5/}
}
TY  - JOUR
AU  - Faenzi, Daniele
TI  - Cohomology of Tango bundle on $\mathbb{P}^5$
JO  - Bollettino della Unione matematica italiana
PY  - 2006
SP  - 319
EP  - 326
VL  - 9B
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_2_a5/
LA  - it
ID  - BUMI_2006_8_9B_2_a5
ER  - 
%0 Journal Article
%A Faenzi, Daniele
%T Cohomology of Tango bundle on $\mathbb{P}^5$
%J Bollettino della Unione matematica italiana
%D 2006
%P 319-326
%V 9B
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_2_a5/
%G it
%F BUMI_2006_8_9B_2_a5
Faenzi, Daniele. Cohomology of Tango bundle on $\mathbb{P}^5$. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 319-326. https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_2_a5/

[Bea00] Arnaud Beauville, Determinantal hypersurfaces, Michigan Math. J. 48 (2000), 39-64.

[BGS87] Ragnar-Olaf Buchweitz - Gert-Martin Greuel - Frank-Olaf Schreyer, Cohen-Macaulay modules on hypersurface singularities. II, Invent. Math. 88 (1987), no. 1, 165-182. | fulltext EuDML

[DMS92] Wolfram Decker - Nicolae Manolache - Frank-Olaf Schreyer, Geometry of the Horrocks bundle on $\mathbb{P}^5$, Complex projective geometry (Trieste, 1989/ Bergen, 1989), London Math. Soc. Lecture Note Ser., vol. 179, Cambridge Univ. Press, Cambridge, 1992, pp. 128-148. | Zbl

[Fae03] Daniele Faenzi, A Geometric Construction of Tango Bundle on $\mathbb{P}^5$, Kodai Mathematical Journal 27 (2004), no. 1, 1-6. | Zbl

[GS] Daniel R. Grayson - Michael E. Stillman, Macaulay 2, a software system for research in algebraic geometry, Available at http://www.math.uiuc.edu/Macaulay2/.

[Hor78] Geoffrey Horrocks, Examples of rank three vector bundles on five-dimensional projective space, J. London Math. Soc. (2) 18 (1978), no. 1, 15-27. | Zbl

[Jan87] Jens Carsten Jantzen, Representations of algebraic groups, Pure and Applied Mathematics, vol. 131, Academic Press Inc., Boston, MA, 1987. | Zbl

[Kap86] Mikhail M. Kapranov, Derived category of coherent bundles on a quadric, Funktsional. Anal. i Prilozhen. 20 (1986), no. 2, 67; English translation in Funct. Anal. Appl. 20 (1986), 141-142.

[Nag62] Masayoshi Nagata, Complete reducibility of rational representations of a matric group, J. Math. Kyoto Univ. 1 (1961/1962), 87-99. | Zbl

[Ott90] Giorgio Ottaviani, On Cayley bundles on the five-dimensional quadric, Boll. Un. Mat. Ital. A (7) 4 (1990), no. 1, 87-100. | Zbl

[Tan76] Hiroshi Tango, On morphisms from projective space $P^n$ to the Grassmann variety $\text{Gr}(n, d)$, J. Math. Kyoto Univ. 16 (1976), no. 1, 201-207. | Zbl