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6. New applications of Kollar’s and Totaro’s techniques


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      Problem 6.1.

      Is the very general hyperusrfae of degree $d\geq 2 \lceil(n+3)/3\rceil$ not rational / stably rational / ruled in char $p>0$ for $p>>0$?


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          Problem 6.2.

          Can we improve those techniques to find differential form for lower degree hypersurfaces?


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              Problem 6.3.

              Can we find new exmaples of unirational varieties that have non-vanishing differential forms?


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                  Problem 6.4.

                  Look for new applications of Kollár / Totaro’s techique.


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                      Problem 6.5.

                      Find an example of varieties which are degenerations of Fano hypersurfaces with $H^{i}(\mathcal{O}_{X})\neq 0$ for some $i$. Try to construct varieties with non-trivial Brawer classes.

                          Cite this as: AimPL: Rational subvarieties in positive characteristic, available at http://aimpl.org/ratsubvarpos.