Embedding of a compactified Jacobian and theta divisors

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
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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