Abstract
The aim of this short note is to define the universal cubic fourfold over certain loci of their moduli space. Then, we propose two methods to prove that it is unirational over the Hassett divisors \( \mathcal{C}_{d} \), in the range 8 ≤ d ≤ 42. By applying inductively this argument, we are able to show that, in the same range of values, \( \mathcal{C}_{d,n} \) is unirational for all integer values of n. Finally, we observe that for explicit infinitely many values of d, the universal cubic fourfold over \( \mathcal{C}_{d} \) can not be unirational.
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Awada, H., Bolognesi, M. (2021). Unirationality of Certain Universal Families of Cubic Fourfolds. In: Farkas, G., van der Geer, G., Shen, M., Taelman, L. (eds) Rationality of Varieties. Progress in Mathematics, vol 342. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-75421-1_4
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DOI: https://doi.org/10.1007/978-3-030-75421-1_4
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Publisher Name: Birkhäuser, Cham
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