Hilbert schemes of two points on K3 surfaces and certain rational cubic fourfolds

Abstract

In this article, we check that Fano schemes of lines on certain rational cubic fourfolds are birational to Hilbert schemes of two points on K3 surfaces.

Keywords:

• Algebraic geometry
• cubic fourfold
• K3 surface
• rationality problem

MATHEMATICS SUBJECT CLASSIFICATION:

• 14E08
• 14J28
• 14J70

Acknowledgements

I would like to thank to Nicolas Addington for the advice for Proposition 2.3. I would like to thanks to my former advisor Yukinobu Toda.

Additional information

Funding

The part of this work was supported by the program for Leading Graduate Schools, MEXT, Japan and Grant-in-Aid for JSPS Research Fellow 15J08505. This work is supported by Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) in RIKEN.