Simplicity of generic Steiner bundles

Maria Chiara Brambilla

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 3, page 723-735
  • ISSN: 0392-4041

Abstract

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A Steiner bundle E on P n has a linear resolution of the form 0 → O ⁢ - 1 s → O t → E → 0 . In this paper we prove that a generic Steiner bundle E is simple if and only if χ ⁢ End ⁢ E is less or equal to 1. In particular we show that either E is exceptional or it satisfies the inequality t ≤ n + 1 + n + 1 2 - 4 2 ⁢ s .

How to cite

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Brambilla, Maria Chiara. "Simplicity of generic Steiner bundles." Bollettino dell'Unione Matematica Italiana 8-B.3 (2005): 723-735. <http://eudml.org/doc/195093>.

@article{Brambilla2005,
abstract = {A Steiner bundle $E$ on $\mathbb\{P\}^\{n\}$ has a linear resolution of the form $0 \rightarrow \mathcal\{O\}(-1)^\{s\}\rightarrow \mathcal\{O\}^\{t\}\rightarrow E \rightarrow 0$. In this paper we prove that a generic Steiner bundle $E$ is simple if and only if $\chi (\mathrm\{End\} E)$ is less or equal to 1. In particular we show that either $E$ is exceptional or it satisfies the inequality $t\leq \left( \frac\{n+1+\sqrt\{(n+1)^\{2\}-4\}\}\{2\} \right)s$.},
author = {Brambilla, Maria Chiara},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {723-735},
publisher = {Unione Matematica Italiana},
title = {Simplicity of generic Steiner bundles},
url = {http://eudml.org/doc/195093},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Brambilla, Maria Chiara
TI - Simplicity of generic Steiner bundles
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/10//
PB - Unione Matematica Italiana
VL - 8-B
IS - 3
SP - 723
EP - 735
AB - A Steiner bundle $E$ on $\mathbb{P}^{n}$ has a linear resolution of the form $0 \rightarrow \mathcal{O}(-1)^{s}\rightarrow \mathcal{O}^{t}\rightarrow E \rightarrow 0$. In this paper we prove that a generic Steiner bundle $E$ is simple if and only if $\chi (\mathrm{End} E)$ is less or equal to 1. In particular we show that either $E$ is exceptional or it satisfies the inequality $t\leq \left( \frac{n+1+\sqrt{(n+1)^{2}-4}}{2} \right)s$.
LA - eng
UR - http://eudml.org/doc/195093
ER -

References

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  1. ANCONA, V. - OTTAVIANI, G., Stability of special instanton bundles on P 2 ⁢ n + 1 , Trans. Amer. Math. Soc., 341 (1994), 677-693, . Zbl0810.14007MR1136544
  2. DOLGACHEV, I. - KAPRANOV, M., Arrangements of hyperplanes and vector bundles on P 2 ⁢ n , Duke Math. J., 71 (1993), 633-664. Zbl0804.14007MR1240599
  3. DREÂZET, J.-M. - LE POTIER, J., Fibrés stables et fibrés exceptionnels sur P 2 , Ann. Sci. École Norm. Sup. (4), 18 (1985), 193-243. Zbl0586.14007MR816365
  4. LENSTRA, H. W., Solving the Pell equation, Notices Amer. Math. Soc., 49 (2002), 182-192. Zbl1126.11312MR1875156
  5. OKONEK, C. - SCHNEIDER, M. - SPINDLER, H., Vector bundles on complex projective spaces, volume 3 of Progress in Mathematics, BirkhäuserBoston, Mass., 1980. Zbl0438.32016MR561910
  6. RUDAKOV, A. N., Markov numbers and exceptional bundles on P 2 ⁢ n , Izv. Akad. Nauk SSSR Ser. Mat., 52 (1988), 100-112, 240. Zbl0661.14017MR936525
  7. RUDAKOV, A. N., Helices and vector bundles, volume 148 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1990. Zbl0727.00022MR1074777
  8. SAMUEL, P., Théorie algébrique des nombres, Hermann, Paris, 1967. Zbl0239.12001MR215808

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