Some results on the compactified Jacobian of a nodal curve

Usha N. Bhosle () and A. J. Parameswaran ()
Additional contact information
Usha N. Bhosle: Indian Statistical Institute
A. J. Parameswaran: Tata Institute of Fundamental Research

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 105-122

Abstract: Abstract Let Y be an integral nodal curve. We show that the connected component of the moduli space of torsion free sheaves of rank 1 on the compactified Jacobian $${\bar{J}}(Y)$$ J ¯ ( Y ) of Y, which contains Pic $$^0 {\bar{J}}(Y)$$ 0 J ¯ ( Y ) , is isomorphic to $${\bar{J}}(Y)$$ J ¯ ( Y ) under the map induced by the Abel–Jacobi embedding of Y in $${\bar{J}}(Y)$$ J ¯ ( Y ) . We determine the Chern classes (in Chow group) of the Picard bundles on the desingularisation of the compactified Jacobian over a nodal curve Y. We study the relation between the singular cohomology of $${\bar{J}}(Y)$$ J ¯ ( Y ) , $${\tilde{J}}(Y)$$ J ~ ( Y ) and J(X) and use it to determine the singular cohomology of the compactified Jacobian of an integral nodal curve. We prove that the compactified Jacobian of an integral nodal curve with k nodes is homeomorphic to the product of the Jacobian of the normalisation $$X_0$$ X 0 and k rational nodal curves of arithmetic genus 1.

Keywords: Compactified Jacobian; Singular cohomology; Picard bundles; Chern classes (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-022-00349-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:55:y:2024:i:1:d:10.1007_s13226-022-00349-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-022-00349-z

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().