Frobenius split anticanonical divisors
arXiv:1912.07231
Abstract
In this note I extend two theorems of Sommese regarding abelian varieties to arbitrary characteristic; that an abelian variety cannot be an ample divisor in a smooth projective variety and that a cone over an abelian variety of dimension at least two is not smoothable.
to appear in "Integrable systems and algebraic geometry", vol.1-2 London Math Society Lecture Notes Series 458-459 (Cambridge University Press)