Differentials of Cox rings: Jaczewski's theorem revisited

A Characterization of Toric Varieties in Characteristicp

“…Remark. Theorem 1.5 from [KW11] assumes that the characteristic of k is zero. This is however not necessary.…”

“…We may expect Theorem 1 to hold more generally for X proper. However, our proof uses the characterization of toric varieties in terms of their Cox rings in the form stated in [KW11] which requires X to be projective. It is worth noting that similar characterizations have been obtained [BH07, Corollary 4.4] for X satisfying the A 2 condition: every two points have a common affine neighborhood.…”

On characterization of toric varieties

“…To begin with, we mention the recent paper [17] (which elaborates on [14]), where an arbitrary smooth complete toric variety T is characterized by the property that certain sheaf R T ∈ Ext 1 (O ⊕h 1,1 (X,C) T…”