Bhosle, Usha N
(2018)
*Embedding of a compactified Jacobian and theta divisors.*
In: MANUSCRIPTA MATHEMATICA, 157
(3-4).
pp. 361-385.

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## Abstract

Using a general stable vector bundle, we give an embedding aY of the compactified Jacobian J (Y) of an integral nodal curve Y into themoduli spaceUY (r, d) of semistable torsion free sheaves of rank r and degree d on Y. We also give an embedding of the normalisation J (Y) of J (Y) in the normalisation P(r, d) of UY (r, d). We determine a relation between the restriction of the theta line bundle on P(r, d) to J (Y) and the theta line bundle on J (Y). We show that the restriction of the Picard bundle Er, d on UY (r, d) to J (Y) is stable with respect to any theta divisor.J (Y) on J (Y) if d > r (2g - 1) and it is semistable if d = r (2g - 1). Finally we prove some results on natural cohomology.

Item Type: | Journal Article |
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Publication: | MANUSCRIPTA MATHEMATICA |

Publisher: | SPRINGER HEIDELBERG |

Additional Information: | Copy right for this article belong to SPRINGER HEIDELBERG |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 15 Oct 2018 15:24 |

Last Modified: | 15 Oct 2018 15:24 |

URI: | http://eprints.iisc.ac.in/id/eprint/60873 |

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