The Wirtinger-type integral for a genus two curve

The Wirtinger integral is one of the integral representations of the Gauss hypergeometric function. Its integrand can be regarded as a multivalued function on an elliptic curve. In this paper, we study an analogue of the Wirtinger integral on a hyperelliptic curve of genus two, introduced by Mizutani and Watanabe. We investigate the associated twisted homology and cohomology groups using the hyperelliptic involution and intersection forms.

💡 Research Summary

The paper investigates a genus‑two analogue of the classical Wirtinger integral, originally known as an integral representation of the Gauss hypergeometric function on an elliptic curve. The authors consider the hyperelliptic curve
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