On the rationality problem for low degree hypersurfaces

2024/09/19 by Lange, Jan, Schreieder, Stefan · 2 citations
#14C25 #14E08 #14J70 #14M20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2409.12834

Abstract

We show that a very general hypersurface of degree d at least 4 and dimension at most (d+1)2^d-4 over a field of characteristic different from 2 does not admit a decomposition of the diagonal; hence, it is neither stably nor retract rational, nor \mathbbA¹-connected. Similar results hold in characteristic 2 under a slightly weaker degree bound. This improves earlier results by the second named author and Moe.

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