### Abstract

We show that over some smooth projective varieties every semistable Higgs logarithmic vector bundle is semistable in the ordinary sense, hence satisfies Bogomolov inequality. More generaly, we prove that semistable Higgs parabolic vector bundles of rank two over smooth projective varieties of dimension ≥ 2 satisfy the "parabolic" 'Bogomolov inequality.

Original language | English |
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Pages (from-to) | 423-436 |

Number of pages | 14 |

Journal | Manuscripta Mathematica |

Volume | 100 |

Issue number | 4 |

Publication status | Published - Dec 1999 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Manuscripta Mathematica*,

*100*(4), 423-436.

**Bogomolov inequality for Higgs parabolic bundles.** / Anchouche, B.

Research output: Contribution to journal › Article

*Manuscripta Mathematica*, vol. 100, no. 4, pp. 423-436.

}

TY - JOUR

T1 - Bogomolov inequality for Higgs parabolic bundles

AU - Anchouche, B.

PY - 1999/12

Y1 - 1999/12

N2 - We show that over some smooth projective varieties every semistable Higgs logarithmic vector bundle is semistable in the ordinary sense, hence satisfies Bogomolov inequality. More generaly, we prove that semistable Higgs parabolic vector bundles of rank two over smooth projective varieties of dimension ≥ 2 satisfy the "parabolic" 'Bogomolov inequality.

AB - We show that over some smooth projective varieties every semistable Higgs logarithmic vector bundle is semistable in the ordinary sense, hence satisfies Bogomolov inequality. More generaly, we prove that semistable Higgs parabolic vector bundles of rank two over smooth projective varieties of dimension ≥ 2 satisfy the "parabolic" 'Bogomolov inequality.

UR - http://www.scopus.com/inward/record.url?scp=0033269259&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033269259&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033269259

VL - 100

SP - 423

EP - 436

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 4

ER -