On two rationality conjectures for cubic fourfolds

By Nicolas Addington. 2014

75 citations recorded by the source corpus.

Motivated by the question of rationality of cubic fourfolds, we show that a cubic X has an associated K3 surface in the sense of Hassett if and only if the variety F of lines on X is birational to a moduli space of sheaves on a K3 surface, but that having F birational to Hilb^2(K3) is more restrictive. We compare the loci in the moduli space of cubics where each condition is satisfied.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7786513b3223c9c69934dc9b9be769d9bad13c76

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Cubic Fourfolds, K3 Surfaces, and Rationality Questions (2016, background): “rational invariant of holomorphic symplectic manifolds but α(K74) ≃ 6 2 2 −24 22 BRENDANHASSETT is not isomorphic to the Picard lattice of the Hilbert scheme Pic(S[2]) ≃ 74 0 0 −2 . Addington [Add14] gives a systematic discussion of this issue. 3.6. Derived equivalence and Cremona transformation”
On the universal $CH_0$ group of cubic hypersurfaces (2014, background): “open problem to prove that there exist irrational cubic fourfolds. Some precise conjectures concerning the rationality of cubic fourfolds have been formulated and compared (see [14], [17], [2], [12], [1]), the strongest (conjecturally) necessary condition has been recently described by Galkin and Sh”