# 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}
}
• C. Athorne
• Published 22 August 2008
• Mathematics
• Journal of Physics A: Mathematical and Theoretical
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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### Determinants and matrices

\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 -