26 citations · 97 across the 17 of their papers we have counts for
25 papers
Very general quartic sixfolds are not stably rational
John Christian Ottem
We prove that a very general quartic sixfold admits no decomposition of the diagonal, and in particular is not stably rational. The proof uses specialization to an explicit quartic…
Fano varieties with torsion in the third cohomology group
John Christian Ottem, Jørgen Vold Rennemo
We construct first examples of Fano varieties with torsion in their third cohomology group. The examples are constructed as double covers of linear sections of rank loci of symmetr…
Planes in cubic fourfolds
Alex Degtyarev, Ilia Itenberg, John Christian Ottem
We show that the maximal number of planes in a complex smooth cubic fourfold in is , realized by the Fermat cubic only; the maximal number of real planes in a…
A refinement of the motivic volume, and specialization of birational types
Johannes Nicaise, John Christian Ottem
We construct an upgrade of the motivic volume by keeping track of dimensions in the Grothendieck ring of varieties. This produces a uniform refinement of the motivic volume and its…
Two coniveau filtrations
Olivier Benoist, John Christian Ottem
A cohomology class of a smooth complex variety of dimension has coniveau if it vanishes in the complement of a closed subvariety of codimension , and has stron…
Tropical degenerations and stable rationality
Johannes Nicaise, John Christian Ottem
We use the motivic obstruction to stable rationality introduced by Shinder and the first-named author to establish several new classes of stably irrational hypersurfaces and comple…