# Identities for hyperelliptic ℘-functions of genus one, two and three in covariant form

@article{Athorne2008IdentitiesFH, title={Identities for hyperelliptic ℘-functions of genus one, two and three in covariant form}, author={Chris Athorne}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2008}, volume={41}, pages={415202} }

We give a covariant treatment of the quadratic differential identities satisfied by the ℘-functions on the Jacobian of smooth hyperelliptic curves of genus ⩽3.

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$$\left[ {\begin{array}{*{20}{c}} {10} \\ { - v{{a}^{{ - 1}}}1} \\ \end{array} } \right]\left[ {\begin{array}{*{20}{c}} {au} \\ {vb} \\ \end{array} } \right]\left[ {\begin{array}{*{20}{c}} {1 -…