Some results on the compactified Jacobian of a nodal curve
Publication details: New Delhi Springer 2024Edition: Vol.55(1), MarDescription: 105-122pSubject(s): Online resources: In: Indian journal of pure and applied mathematicsSummary: 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 of Y, which contains Pic, is isomorphic to under the map induced by the Abel–Jacobi embedding of Y in . 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 , 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 and k rational nodal curves of arithmetic genus 1.| Item type | Current library | Status | Barcode | |
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School of Engineering & Technology Archieval Section | Not for loan | 2024-1553 |
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 of Y, which contains Pic, is isomorphic to under the map induced by the Abel–Jacobi embedding of Y in . 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 , 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 and k rational nodal curves of arithmetic genus 1.
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