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arXiv · 1706.07462

The Rees algebra of a two-Borel ideal is Koszul

Michael DiPasquale·Christopher A. Francisco·Jeffrey Mermin·Jay Schweig·Gabriel Sosa
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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 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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Michael DiPasquale, Christopher A. Francisco, Jeffrey Mermin, Jay Schweig, Gabriel Sosa. 2017-06-22. The Rees algebra of a two-Borel ideal is Koszul. https://arxiv.org/abs/1706.07462

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