Which quartic double solids are rational?

Ivan Cheltsov; Victor Przyjalkowski; Constantin Shramov

doi:10.1090/jag/730

Which quartic double solids are rational?

Ivan Cheltsov, Victor Przyjalkowski, Constantin Shramov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the rationality problem for nodal quartic double solids. In particular,
we prove that nodal quartic double solids with at most six singular points are
irrational, and nodal quartic double solids with at least eleven singular points are rational.

Original language	English
Pages (from-to)	201-243
Number of pages	33
Journal	Journal of Algebraic Geometry
Volume	28
Issue number	2
Early online date	7 Dec 2018
DOIs	https://doi.org/10.1090/jag/730
Publication status	Published - Apr 2019

Keywords / Materials (for Non-textual outputs)

math.AG
14E08, 14M20, 14J45

Access to Document

10.1090/jag/730

JAG1345Accepted author manuscript, 444 KBLicence: Creative Commons: Attribution-NonCommercial-ShareAlike (CC BY-NC-SA)

Ivan Cheltsov
- School of Mathematics - Personal Chair in Birational Geometry
Person: Academic: Research Active

Cite this

@article{a10d94b5cd3b4d1686703c8b797ac524,

title = "Which quartic double solids are rational?",

abstract = "We study the rationality problem for nodal quartic double solids. In particular, we prove that nodal quartic double solids with at most six singular points are irrational, and nodal quartic double solids with at least eleven singular points are rational.",

keywords = "math.AG, 14E08, 14M20, 14J45",

author = "Ivan Cheltsov and Victor Przyjalkowski and Constantin Shramov",

note = "30 pages",

year = "2019",

month = apr,

doi = "10.1090/jag/730",

language = "English",

volume = "28",

pages = "201--243",

journal = "Journal of Algebraic Geometry",

issn = "1056-3911",