The Severi line equality, already known in characteristic zero, is now characterized in all characteristics: equality holds exactly for canonical models that are flat double covers of Abelian surfaces.
and Buchbaum, D.: Homological dimension in local rings , Trans- action of the A
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Surfaces on the Severi line in positive characteristics
The Severi line equality, already known in characteristic zero, is now characterized in all characteristics: equality holds exactly for canonical models that are flat double covers of Abelian surfaces.