Reference : On 1-dimensional sheaves on projective plane |

Scientific Presentations in Universities or Research Centers : Scientific presentation in universities or research centers | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/23680 | |||

On 1-dimensional sheaves on projective plane | |

English | |

Iena, Oleksandr [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Jan-2016 | |

International | |

Workshop - Higgs bundles and Hitchin system - VBAC2016 | |

from 11-01-2016 to 15-01-2016 | |

Lausanne | |

Switzerland | |

[en] Simpson moduli spaces ; coherent sheaves ; vector bundles on curves ; singular sheaves | |

[en] Let M be the Simpson moduli space of semistable sheaves on the projective plane
with fixed linear Hilbert polynomial P(m)=dm+c. A generic sheaf in M is a vector bundle on its Fitting support, which is a planar projective curve of degree d. The sheaves that are not vector bundles on their support constitute a closed subvariety M' in M. We study the geometry of M' in the case of Hilbert polynomials dm-1 (for d bigger than 3) and demonstrate that M' is a singular variety of codimension 2 in M. We speculate on how the question we study is related to recompactifying of the Simpson moduli spaces by vector bundles. | |

Researchers ; Professionals | |

http://hdl.handle.net/10993/23680 |

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