Mathematische Annalen

, Volume 342, Issue 4, pp 885–902 | Cite as

On the Poincare formula and the Riemann singularity theorem over nodal curves

  • Usha N. BhosleEmail author
  • A. J. Parameswaran


The symmetric powers of a smooth curve determine effective cycles in the Jacobian of the curve. The classical Poincare formula expresses these cycles in terms of the powers of the theta divisor of the Jacobian. Here we prove an analogue of this well-known Poincare formula for the desingularisation of the compactified Jacobian of an irreducible nodal curve with arbitrary number of nodes. We also prove an analogue of the Riemann singularity theorem and show that these effective cycles are normal.


Exact Sequence Line Bundle Singular Locus Cartier Divisor Nodal Curve 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.School of MathematicsTata Institute of Fundamental ResearchMumbaiIndia

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