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The goal of this work is to consider some geometric properties ofgeometrically irreducible subschemes on degenerations of separably rationallyconnected varieties. It is known that these geometrically irreduciblesubschemes exist when the ground field has characteristic zero or contains analgebraically closed subfield. In this note, we show that the dimension of thisgeometrically irreducible subscheme has a lower bound by the Fano index of thegeneric fiber.

On Subvarieties of Degenerations of Separably Rationally Connected Varieties