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
Abstract

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.

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