The Rees algebra of a two-Borel ideal is Koszul

DiPasquale, Michael; Francisco, Christopher; Mermin, Jeffrey; Schweig, Jay; Sosa, Gabriel

doi:10.1090/proc/13966

The Rees algebra of a two-Borel ideal is Koszul
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by Michael DiPasquale, Christopher A. Francisco, Jeffrey Mermin, Jay Schweig and Gabriel Sosa PDF

Proc. Amer. Math. Soc. 147 (2019), 467-479 Request permission

Abstract:

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 Gröbner 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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