Regularity in Linear Degenerations of Flag Variety

Abstract In this article we investigate the regularity properties of linear degenerations of flag varieties. We classify the linear degenerations of (partial) flag varieties that are smooth. Furthermore, we study the singular locus of irreducible degenerations and provide estimates for its dimension. We also introduce a new stratification of the total space of representations. Within each stratum, we identify the loci corresponding to flat and flat irreducible degenerations. As a consequence of our results, we show that irreducible linear degenerations are normal varieties.