Degenerations of Gushel–Mukai fourfolds, with a view towards irrationality proofs

Abstract

We study a certain class of degenerations of Gushel-Mukai fourfolds as conic bundles, which we call tame degenerations and which are natural if one wants to prove that very general Gushel-Mukai fourfolds are irrational using the degeneration method due to Voisin, Colliot-Thélène-Pirutka, Totaro et al. However, we prove that no such tame degenerations exist.

Symmetric locally free resolutions and rationality problems

“…The relation between Verra and nodal Gushel-Mukai fourfolds in Corollary 1.4 was obtained independently in [13] with different methods. Also, recall that it was proved in [10,Theorem 4.5] that a general nodal Gushel-Mukai threefold is birational to a Verra threefold (cf [7]).…”