Prym varieties and moduli of polarized Nikulin surfaces

Gavril Farkas; Alessandro Verra

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arXiv · 1503.05967

Prym varieties and moduli of polarized Nikulin surfaces

Gavril Farkas·Alessandro Verra

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Abstract

We present a structure theorem for the moduli space R_7 of Prym curves of genus 7 as a projective bundle over the moduli space of 7-nodal rational curves. The existence of this parametrization implies the unirationality of R_7 and that of the moduli space of Nikulin surfaces of genus 7, as well as the rationality of the moduli space of Nikulin surfaces of genus 7 with a distinguished line. Using the results in genus 7, we then establish that R_8 is uniruled.

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Gavril Farkas, Alessandro Verra. 2015-12-08. Prym varieties and moduli of polarized Nikulin surfaces. https://arxiv.org/abs/1503.05967

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