Decomposability criterion for linear sheaves

Marcos Jardim; Vitor Silva

Open Mathematics (2012)

  • Volume: 10, Issue: 4, page 1292-1299
  • ISSN: 2391-5455

Abstract

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We establish a decomposability criterion for linear sheaves on ℙn. Applying it to instanton bundles, we show, in particular, that every rank 2n instanton bundle of charge 1 on ℙn is decomposable. Moreover, we provide an example of an indecomposable instanton bundle of rank 2n − 1 and charge 1, thus showing that our criterion is sharp.

How to cite

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Marcos Jardim, and Vitor Silva. "Decomposability criterion for linear sheaves." Open Mathematics 10.4 (2012): 1292-1299. <http://eudml.org/doc/269156>.

@article{MarcosJardim2012,
abstract = {We establish a decomposability criterion for linear sheaves on ℙn. Applying it to instanton bundles, we show, in particular, that every rank 2n instanton bundle of charge 1 on ℙn is decomposable. Moreover, we provide an example of an indecomposable instanton bundle of rank 2n − 1 and charge 1, thus showing that our criterion is sharp.},
author = {Marcos Jardim, Vitor Silva},
journal = {Open Mathematics},
keywords = {Linear sheaves; Instanton bundles; Representations of quivers; instanton bundles; quiver representations; decomposability criterions for sheaves; linear sheaves},
language = {eng},
number = {4},
pages = {1292-1299},
title = {Decomposability criterion for linear sheaves},
url = {http://eudml.org/doc/269156},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Marcos Jardim
AU - Vitor Silva
TI - Decomposability criterion for linear sheaves
JO - Open Mathematics
PY - 2012
VL - 10
IS - 4
SP - 1292
EP - 1299
AB - We establish a decomposability criterion for linear sheaves on ℙn. Applying it to instanton bundles, we show, in particular, that every rank 2n instanton bundle of charge 1 on ℙn is decomposable. Moreover, we provide an example of an indecomposable instanton bundle of rank 2n − 1 and charge 1, thus showing that our criterion is sharp.
LA - eng
KW - Linear sheaves; Instanton bundles; Representations of quivers; instanton bundles; quiver representations; decomposability criterions for sheaves; linear sheaves
UR - http://eudml.org/doc/269156
ER -

References

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  1. [1] Fløystad G., Monads on projective spaces, Comm. Algebra, 2000, 28(12), 5503–5516 http://dx.doi.org/10.1080/00927870008827171 Zbl0977.14007
  2. [2] Horrocks G., Vector bundles on the punctured spectrum of a local ring, Proc. London Math. Soc., 1964, 14, 689–713 http://dx.doi.org/10.1112/plms/s3-14.4.689 Zbl0126.16801
  3. [3] Jardim M., Instanton sheaves on complex projective spaces, Collect. Math., 2006, 57(1), 69–91 Zbl1095.14040
  4. [4] Jardim M., Miró-Roig R.M., On the semistability of instanton sheaves over certain projective varieties, Comm. Algebra, 2008, 36(1), 288–298 http://dx.doi.org/10.1080/00927870701665503 Zbl1131.14046
  5. [5] Kac V.G., Infinite root systems, representations of graphs and invariant theory, Invent. Math., 1980, 56(1), 57–92 http://dx.doi.org/10.1007/BF01403155 Zbl0427.17001
  6. [6] Okonek Chr., Schneider M., Spindler H., Vector Bundles on Complex Projective Spaces, Progr. Math., 3, Birkhäuser, Boston, 1980 http://dx.doi.org/10.1007/978-3-0348-0151-5 Zbl0438.32016

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