#### Vol. 11, No. 7, 2017

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
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 $\mathsc{C}$ contains a divisor ${\mathsc{C}}_{42}$ 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 ${\mathsc{C}}_{42}$ is uniruled.

##### Keywords
cubic fourfold, K3 surface, rational surface, unirational parametrization
##### Mathematical Subject Classification 2010
Primary: 14E08
Secondary: 14J26, 14J35, 14J70, 14M20