A classification theorem on Fano bundles

Roberto Muñoz[1]; Luis E. Solá Conde[1]; Gianluca Occhetta[2]

  • [1] ESCET Departamento de Matemática Aplicada Universidad Rey Juan Carlos Campus de Móstoles C/Tulipan S/N, 28933 Móstoles Madrid (Espagne)
  • [2] Università di Trento Dipartimento di Matematica Via Sommarive 14, I-38123 Povo (TN), (Italie)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 1, page 341-373
  • ISSN: 0373-0956

Abstract

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In this paper we classify rank two Fano bundles ℰ on Fano manifolds satisfying H 2 ( X , ℤ ) ≅ H 4 ( X , ℤ ) ≅ ℤ . The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization ℙ ( ℰ ) , that allows us to obtain the cohomological invariants of X and ℰ . As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.

How to cite

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Muñoz, Roberto, Solá Conde, Luis E., and Occhetta, Gianluca. "A classification theorem on Fano bundles." Annales de l’institut Fourier 64.1 (2014): 341-373. <http://eudml.org/doc/275606>.

@article{Muñoz2014,
abstract = {In this paper we classify rank two Fano bundles $\{\mathcal\{E\}\}$ on Fano manifolds satisfying $H^2(X,\{\mathbb\{Z\}\})\cong H^4(X,\{\mathbb\{Z\}\})\cong \{\mathbb\{Z\}\}$. The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization $\{\mathbb\{P\}\}(\{\mathcal\{E\}\})$, that allows us to obtain the cohomological invariants of $X$ and $\{\mathcal\{E\}\}$. As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.},
affiliation = {ESCET Departamento de Matemática Aplicada Universidad Rey Juan Carlos Campus de Móstoles C/Tulipan S/N, 28933 Móstoles Madrid (Espagne); ESCET Departamento de Matemática Aplicada Universidad Rey Juan Carlos Campus de Móstoles C/Tulipan S/N, 28933 Móstoles Madrid (Espagne); Università di Trento Dipartimento di Matematica Via Sommarive 14, I-38123 Povo (TN), (Italie)},
author = {Muñoz, Roberto, Solá Conde, Luis E., Occhetta, Gianluca},
journal = {Annales de l’institut Fourier},
keywords = {vector bundles; Fano manifolds; vector bundle; Fano manifold},
language = {eng},
number = {1},
pages = {341-373},
publisher = {Association des Annales de l’institut Fourier},
title = {A classification theorem on Fano bundles},
url = {http://eudml.org/doc/275606},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Muñoz, Roberto
AU - Solá Conde, Luis E.
AU - Occhetta, Gianluca
TI - A classification theorem on Fano bundles
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 1
SP - 341
EP - 373
AB - In this paper we classify rank two Fano bundles ${\mathcal{E}}$ on Fano manifolds satisfying $H^2(X,{\mathbb{Z}})\cong H^4(X,{\mathbb{Z}})\cong {\mathbb{Z}}$. The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization ${\mathbb{P}}({\mathcal{E}})$, that allows us to obtain the cohomological invariants of $X$ and ${\mathcal{E}}$. As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.
LA - eng
KW - vector bundles; Fano manifolds; vector bundle; Fano manifold
UR - http://eudml.org/doc/275606
ER -

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