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A note on Nikulin surfaces and their moduli spaces

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Abstract

We study a number of natural linear systems carried by any polarized Nikulin surface of genus g, determine their positivity and establish their Brill–Noether theory. As an application, we compute the classes of some natural effective divisors on the moduli space of Nikulin surfaces, relying upon recent work of Farkas and Rimányi.

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Acknowledgements

This work started thanks to the financial support of the Einstein Foundation and I wish to thank G. Farkas and R. Pandharipande for giving me the opportunity to spend some pleasant time in Berlin. I am warmly thankful to G. Farkas for useful conversations around these topics.

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  1. Lehrstuhl für Algebra und Zahlentheorie, Institut für Mathematik, Universität Augsburg, 86135, Augsburg, Deutschland

    Marco Ramponi

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  1. Marco Ramponi
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Correspondence to Marco Ramponi.

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Ramponi, M. A note on Nikulin surfaces and their moduli spaces. Math. Z. 295, 761–774 (2020). https://doi.org/10.1007/s00209-019-02367-w

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  • DOI: https://doi.org/10.1007/s00209-019-02367-w

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