Cohomology of Tango bundle on $\mathbb{P}^5$

Faenzi, Daniele

Cohomology of Tango bundle on

\mathbb{P}^{5}

Faenzi, Daniele

Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006), p. 319-326 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

The Tango bundle $T$ is defined as the pull-back of the Cayley bundle over a smooth quadric $Q_{5}$ in $\mathbb{P}_{6}$ via a map $f$ existing only in characteristic 2 and factorizing the Frobenius $\varphi$ . The cohomology of $T$ is computed in terms of $S\otimes C$ , $\varphi^{*}(C)$ , $\text{Sym}^{2}(C)$ and $C$ , which we handle with Borel-Bott-Weil theorem.

-- 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.

Publié le : 2006-06-01

MR 2233141 | Zbl 1178.14011

@article{BUMI_2006_8_9B_2_319_0,
     author = {Daniele Faenzi},
     title = {Cohomology of Tango bundle on $\mathbb{P}^5$},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {9-A},
     year = {2006},
     pages = {319-326},
     zbl = {1178.14011},
     mrnumber = {2233141},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2006_8_9B_2_319_0}
}

Faenzi, Daniele. Cohomology of Tango bundle on $\mathbb{P}^5$. Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006) pp. 319-326. http://gdmltest.u-ga.fr/item/BUMI_2006_8_9B_2_319_0/

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