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In this paper we describe the notion of a toric supervariety, generalizingthat of a toric variety from the classical setting. We give a combinatorialinterpretation of the category of quasinormal toric supervarieties with one odddimension using decorated polyhedral fans. We then use this interpretation tocalculate some invariants of these supervarieties and extract geometricinformation from them.

Toric supervarieties with one odd dimension