Title | Rational curves and instantons on the Fano threefold Y_5 |

Publication Type | Thesis |

Year of Publication | 2014 |

Authors | Sanna, G |

University | arXiv preprint |

Keywords | Moduli space of vector bundles |

Abstract | This thesis is an investigation of the moduli spaces of instanton bundles on the Fano threefold Y_5 (a linear section of Gr(2,5)). It contains new proofs of classical facts about lines, conics and cubics on Y_5, and about linear sections of Y_5. The main original results are a Grauert-Mülich theorem for the splitting type of instantons on conics, a bound to the splitting type of instantons on lines and an SL_2-equivariant description of the moduli space in charge 2 and 3. Using these results we prove the existence of a unique SL_2-equivariant instanton of minimal charge and we show that for all instantons of charge 2 the divisor of jumping lines is smooth. In charge 3, we provide examples of instantons with reducible divisor of jumping lines. Finally, we construct a natural compactification for the moduli space of instantons of charge 3, together with a small resolution of singularities for it. |

URL | http://urania.sissa.it/xmlui/handle/1963/7482 |

Custom 1 | 7594 |

Custom 2 | Mathematics |

Custom 4 | 1 |

Custom 5 | MAT/02 |

Custom 6 | Submitted by gggsanna@sissa.it (gggsanna@sissa.it) on 2014-12-01T10:51:46Z |

## Rational curves and instantons on the Fano threefold Y_5

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