In this paper, I compute the regularity of the Rees algebra of binomial edge ideals of closed graphs. I obtain a lower bound for the regularity of the Rees algebra of binomial edge ideals. I also present some algebraic properties of the Rees algebra and special fiber ring of binomial edge ideals of closed graphs via algebraic properties of their initial algebra and Sagbi basis theory. I obtain an upper bound for the regularity of the special fiber ring of binomial edge ideals of closed graphs.
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Arvind Kumar (2022) studied this question.
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