Vol. 11, No. 7, 2017

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New cubic fourfolds with odd-degree unirational parametrizations

Kuan-Wen Lai

Vol. 11 (2017), No. 7, 1597–1626

We prove that the moduli space of cubic fourfolds C contains a divisor C42 whose general member has a unirational parametrization of degree 13. This result follows from a thorough study of the Hilbert scheme of rational scrolls and an explicit construction of examples. We also show that C42 is uniruled.

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cubic fourfold, K3 surface, rational surface, unirational parametrization
Mathematical Subject Classification 2010
Primary: 14E08
Secondary: 14J26, 14J35, 14J70, 14M20
Received: 27 September 2016
Revised: 28 April 2017
Accepted: 5 June 2017
Published: 7 September 2017
Kuan-Wen Lai
Department of Mathematics
Brown University
Providence, RI
United States