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arXiv · 1910.07624

Gauss-Manin connection in disguise: Genus two curves

Jin Cao·Hossein Movasati·Shing-Tung Yau
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Abstract

We describe an algebra of meromorphic functions on the Siegel domain of genus two which contains Siegel modular forms for an arithmetic index six subgroup of the symplectic group and it is closed under three canonical derivations of the Siegel domain. The main ingredients of our study are the moduli of enhanced genus two curves, Gauss-Manin connection and the modular vector fields living on such moduli spaces.

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Jin Cao, Hossein Movasati, Shing-Tung Yau. 2020-02-03. Gauss-Manin connection in disguise: Genus two curves. https://arxiv.org/abs/1910.07624

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