Which quartic double solids are rational?

Cheltsov, Ivan; Przyjalkowski, Victor; Shramov, Constantin

doi:10.1090/jag/730

Authors: Ivan Cheltsov, Victor Przyjalkowski and Constantin Shramov
Journal: J. Algebraic Geom. 28 (2019), 201-243
DOI: https://doi.org/10.1090/jag/730
Published electronically: December 7, 2018
MathSciNet review: 3912057
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Abstract | References | Additional Information

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.

References

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Additional Information

Ivan Cheltsov
Affiliation: School of Mathematics, The University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom; National Research University Higher School of Economics, Laboratory of Algebraic Geometry, 6 Usacheva str., Moscow, 119048, Russia
MR Author ID: 607648
Email: i.cheltsov@ed.ac.uk

Victor Przyjalkowski
Affiliation: Steklov Institute of Mathematics, 8 Gubkina str., Moscow 119991, Russia; Russian Federation, Laboratory of Mirror Symmetry, NRU HSE, 6 Usacheva str., Moscow, 119048, Russia
MR Author ID: 741170
Email: victorprz@mi-ras.ru, victorprz@gmail.com

Constantin Shramov
Affiliation: Steklov Institute of Mathematics, 8 Gubkina str., Moscow 119991, Russia; National Research University Higher School of Economics, Laboratory of Algebraic Geometry, 6 Usacheva str., Moscow, 119048, Russia
MR Author ID: 907948
Email: costya.shramov@gmail.com

Received by editor(s): November 15, 2015
Received by editor(s) in revised form: January 31, 2017
Published electronically: December 7, 2018
Additional Notes: The first author was supported by the Russian Academic Excellence Project “5-100” and by the Royal Society grant No. IES/R1/180205. The second author was supported by Laboratory of Mirror Symmetry NRU HSE, RF government grant, ag. No. 14.641.31.0001. The third author was supported by the Russian Academic Excellence Project “5-100”, the grants RFFI 15-01-02158, RFFI 15-01-02164, and the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”. The last two authors are also Young Russian Mathematics award winners and would like to thank its sponsors and jury
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