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arXiv · 2607.22339

Generalizations of the Scorza correspondence

Maria Teresa Ruggiero
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Abstract

We study generalizations of the Scorza correspondence associated with a general $(C,\eta)$ in the moduli space of even spin curves $S_g^+$. We first give a new proof of the smoothness of the classical Scorza curve, originally established by Farkas-Verra. We then introduce higher order analogues of the Scorza correspondence and investigate their geometry. In particular, we compute their classes in the N\'eron-Severi group and study their singularities and genera. Finally, we consider a higher-dimensional version of the construction and focus on the threefold case, where we describe its class and prove a smoothness result outside a naturally defined degeneracy locus.

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Maria Teresa Ruggiero. 2026-07-24. Generalizations of the Scorza correspondence. https://arxiv.org/abs/2607.22339

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