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On Algebraic Theta Divisors and Rational Solutions of the KP Equation

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arxiv 2112.03147 v1 pith:JJ4ERT44 submitted 2021-12-06 math.AG math-phmath.MP

Daniele Agostini , Türkü Özlüm Çelik , John B. Little This is my paper · ORCID
classification math.AGmath-phmath.MP
keywords thetaalgebraicfunctionsdivisorsanalogsclassifycorrespondingcurve
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In this paper we classify the singular curves whose theta divisors in their generalized Jacobians are algebraic, meaning that they are cut out by polynomial analogs of theta functions. We also determine the degree of an algebraic theta divisor in terms of the singularities of the curve. Furthermore, we show a precise relation between such algebraic theta functions and the corresponding tau functions for the KP hierarchy.

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