Cohomology of Tango bundle on 5

Daniele Faenzi

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 2, page 319-326
  • ISSN: 0392-4033

Abstract

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The Tango bundle T is defined as the pull-back of the Cayley bundle over a smooth quadric Q 5 in 6 via a map f existing only in characteristic 2 and factorizing the Frobenius φ . The cohomology of T is computed in terms of S C , φ * ( C ) , Sym 2 ( C ) and C , which we handle with Borel-Bott-Weil theorem.

How to cite

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Faenzi, Daniele. "Cohomology of Tango bundle on $\mathbb{P}^5$." Bollettino dell'Unione Matematica Italiana 9-B.2 (2006): 319-326. <http://eudml.org/doc/289609>.

@article{Faenzi2006,
abstract = {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.},
author = {Faenzi, Daniele},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {319-326},
publisher = {Unione Matematica Italiana},
title = {Cohomology of Tango bundle on $\mathbb\{P\}^5$},
url = {http://eudml.org/doc/289609},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Faenzi, Daniele
TI - Cohomology of Tango bundle on $\mathbb{P}^5$
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/6//
PB - Unione Matematica Italiana
VL - 9-B
IS - 2
SP - 319
EP - 326
AB - 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.
LA - eng
UR - http://eudml.org/doc/289609
ER -

References

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  3. DECKER, WOLFRAM - MANOLACHE, NICOLAE - SCHREYER, FRANK-OLAF, Geometry of the Horrocks bundle on 5 , Complex projective geometry (Trieste, 1989/ Bergen, 1989), London Math. Soc. Lecture Note Ser., vol. 179, Cambridge Univ. Press, Cambridge, 1992, pp. 128-148. Zbl0774.14013
  4. FAENZI, DANIELE, A Geometric Construction of Tango Bundle on 5 , Kodai Mathematical Journal27 (2004), no. 1, 1-6. Zbl1093.14506
  5. GRAYSON, DANIEL R. - STILLMAN, MICHAEL E., Macaulay 2, a software system for research in algebraic geometry, Available at http://www.math.uiuc.edu/Macaulay2/. 
  6. HORROCKS, GEOFFREY, Examples of rank three vector bundles on five-dimensional projective space, J. London Math. Soc. (2) 18 (1978), no. 1, 15-27. Zbl0388.14009
  7. JANTZEN, JENS CARSTEN, Representations of algebraic groups, Pure and Applied Mathematics, vol. 131, Academic Press Inc., Boston, MA, 1987. Zbl0654.20039
  8. KAPRANOV, MIKHAIL M., 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. 
  9. NAGATA, MASAYOSHI, Complete reducibility of rational representations of a matric group, J. Math. Kyoto Univ.1 (1961/1962), 87-99. Zbl0106.25201
  10. OTTAVIANI, GIORGIO, On Cayley bundles on the five-dimensional quadric, Boll. Un. Mat. Ital. A (7) 4 (1990), no. 1, 87-100. Zbl0722.14006
  11. TANGO, HIROSHI, On morphisms from projective space P n to the Grassmann variety Gr ( n , d ) , J. Math. Kyoto Univ.16 (1976), no. 1, 201-207. Zbl0326.14015

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