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Birational geometry of some universal families of n-pointed Fano fourfolds

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Abstract

The object of this note are the moduli spaces of cubic fourfolds (respectively, Gushel–Mukai fourfolds) which contain some special rational surfaces. Under certain hypotheses on the families of such surfaces, we develop a general method to show the unirationality of moduli spaces of n-pointed such fourfolds. We apply this to some codimension-one loci of cubic fourfolds (respectively, Gushel–Mukai fourfolds) which appeared in the literature recently.

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Acknowledgements

We heartfully thank the referees for insightful comments that helped us to improve the paper in an important way. We also thank Michael Hoff for inspiring conversations on these topics.

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Authors and Affiliations

  1. Institut Montpellierain Alexander Grothendieck, CNRS, Université de Montpellier, Case Courrier 051, Place Eugène Bataillon, 34095, Montpellier Cedex 5, France

    Hanine Awada & Michele Bolognesi

  2. Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 5, 95125, Catania, Italy

    Giovanni Staglianò

Authors
  1. Hanine Awada
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  2. Michele Bolognesi
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  3. Giovanni Staglianò
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Correspondence to Michele Bolognesi.

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Awada, H., Bolognesi, M. & Staglianò, G. Birational geometry of some universal families of n-pointed Fano fourfolds. European Journal of Mathematics 8 (Suppl 1), 130–146 (2022). https://doi.org/10.1007/s40879-022-00545-5

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  • DOI: https://doi.org/10.1007/s40879-022-00545-5

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