Torsion orders of Fano hypersurfaces

Torsion orders of Fano hypersurfaces

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Stefan Schreieder, LMU Munich
Fine Hall 110

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We find new lower bounds on the torsion orders of very general Fano hypersurfaces over (uncountable) fields of arbitrary characteristic. Our results imply that unirational parametrizations of most Fano hypersurfaces need to have enormously large degree. Our results also hold in characteristic two, where they solve the rationality problem for hypersurfaces under a logarithmic degree bound, thereby extending a previous result of the speaker from characteristic different from two to arbitrary characteristic.