Publication: Research - peer-review › Journal article

- 10.1016/j.jalgebra.2014.10.051
Final published version

- Sudarshan GurjarSudarshan GurjarInternational Centre for Theoretical Physics (ICTP), TriesteDenmark

The aim of this paper is to prove two basic restriction theorem for principal bundles on smooth projective varieties in arbitrary characteristic generalizing the analogues theorems of Mehta-Ramanathan for vector bundles.

More precisely, let G be a reductive algebraic group over an algebraically closed field k and let X be a smooth, projective variety over k together with a very ample line bundle O(1). The main result of the paper is that if E is a semistable (resp. stable) principal G-bundle on X w.r.t O(1), then the restriction of E to a general, high multi-degree, complete-intersection curve is again semistable (resp. stable).

As easy applications of these theorems we show the openness of semistability (resp. stability) for a family of principal bundles parametrized by a finite-type k-scheme.

More precisely, let G be a reductive algebraic group over an algebraically closed field k and let X be a smooth, projective variety over k together with a very ample line bundle O(1). The main result of the paper is that if E is a semistable (resp. stable) principal G-bundle on X w.r.t O(1), then the restriction of E to a general, high multi-degree, complete-intersection curve is again semistable (resp. stable).

As easy applications of these theorems we show the openness of semistability (resp. stability) for a family of principal bundles parametrized by a finite-type k-scheme.

Original language | English |
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Journal | Journal of Algebra |

Volume | 426 |

Pages (from-to) | 79-91 |

Number of pages | 13 |

ISSN | 0021-8693 |

DOIs | |

State | Published - 2015 |

- Principal bundle, semistability, Quot scheme, Hilbert scheme

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