The Rees algebra of a two-Borel ideal is Koszul
2018
Let $M$ and $N$ be two monomials of the same degree, and let $I$ be the smallest Borel ideal containing $M$ and $N$. We show that the toric ring of $I$ is Koszul by constructing a quadratic Gr\"obner basis for the associated toric ideal. Our proofs use the construction of graphs corresponding to fibers of the toric map. As a consequence, we conclude that the Rees algebra is also Koszul.
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