Singular pencils of quadrics and compactified Jacobians of curves

Bhosle, Usha N. (1990) Singular pencils of quadrics and compactified Jacobians of curves Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 100 (2). pp. 95-102. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/100/2/95-10...

Related URL: http://dx.doi.org/10.1007/BF02880954

Abstract

Let Y be an irreducible nodal hyperelliptic curve of arithmetic genus g such that its nodes are also ramification points (char ≠2). To the curveY, we associate a family of quadratic forms which is dual to a singular pencil of quadrics in P2g+1 with Segre symbol [2...21...1], where the number of 2's is equal to the number of nodes. We show that the compactified Jacobian of Y is isomorphic to the space R of (g-1) dimensional linear subspaces P2g+1 of which are contained in the intersection Q of quadrics of the pencil. We also prove that (under this isomorphism) the generalized Jacobian of Y is isomorphic to the open subset of R consisting of the (g-1) dimensional subspaces not passing through any singular point of Q.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Nodal Hyperelliptic Curve; Compactified Jacobian
ID Code:3416
Deposited On:11 Oct 2010 09:04
Last Modified:16 May 2016 14:13

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