New cubic fourfolds with odd-degree unirational parametrizations

Lai, Kuan-Wen

doi:10.2140/ant.2017.11.1597

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New cubic fourfolds with odd-degree unirational parametrizations

Kuan-Wen Lai

Vol. 11 (2017), No. 7, 1597–1626

DOI: 10.2140/ant.2017.11.1597

Abstract

We prove that the moduli space of cubic fourfolds $C$ contains a divisor $C_{42}$ 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 $C_{42}$ 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

Vol. 11, No. 7, 2017