Abstract
In this section we will define and describe the generalized Jacobian of the simplest singular curves: the curves obtained by identifying 2g points of IP1 in pairs. We will then determine their theta functions and theta divisors. Finally, we will apply this theory to understand analytically and geometrically the limits of the solutions to the KdV equation that were discussed in the previous section, when the hyperelliptic curve becomes singular of the above form.
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© 2007 Birkhäuser Boston
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Mumford, D. (2007). The Generalized Jacobian of a Singular Curve and its Theta Function. In: Tata Lectures on Theta II. Modern Birkhäuser Classics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4578-6_17
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DOI: https://doi.org/10.1007/978-0-8176-4578-6_17
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4569-4
Online ISBN: 978-0-8176-4578-6
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