1. Maximally algebraic potentially irrational cubic fourfolds.
- Author
-
Laza, Radu
- Subjects
LOGICAL prediction ,IRRATIONAL numbers ,MATHEMATICS ,GEOMETRY - Abstract
A well known conjecture due to Hassett asserts that a cubic fourfold X whose transcendental cohomology T
X cannot be realized as the transcendental cohomology of a K3 surface is irrational. Since the geometry of cubic fourfolds is intricately related to the existence of algebraic 2-cycles on them, it is natural to ask for the most algebraic cubic fourfolds X to which this conjecture is still applicable. In this paper, we show that for an appropriate "algebraicity index" κX ∈ Q+ , there exists a unique class of cubics maximizing κX , not having an associated K3 surface; namely, the cubic fourfolds with an Eckardt point (previously investigated in by Laza, Pearlstein, and Zhang [Adv. Math. 340 (2018), pp. 684-722]). Arguably, they are the most algebraic conjecturally irrational cubic fourfolds, and thus a good testing ground for Hassett's irrationality conjecture for cubic fourfolds. [ABSTRACT FROM AUTHOR]- Published
- 2021
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