The maximal unipotent finite quotient, unusual torsion in Fano threefolds, and exceptional Enriques surfaces

The maximal unipotent finite quotient, unusual torsion in Fano threefolds, and exceptional Enriques surfaces

Blog Article

We introduce and study the maximal unipotent finite quotient for algebraic group schemes in positive characteristics.Applied to Picard schemes, this quotient encodes unusual torsion.We here construct integral Fano threefolds where such unusual torsion actually appears.The existence of such threefolds is surprising, because the torsion vanishes for del sequal eclipse 5 battery Pezzo surfaces.

Our construction relies on the theory of exceptional Enriques surfaces, as developed by Ekedahl and Shepherd-Barron.