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Linear syzygies and birational combinatorics

Aron Simis·Rafael H. Villarreal
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Abstract

Let $F$ be a finite set of monomials of the same degree $d\geq 2$ in a polynomial ring $R=k[x_1,...,x_n]$ over an arbitrary field $k$. We give some necessary and/or sufficient conditions for the birationality of the ring extension $k[F]\subset R^{(d)}$, where $R^{(d)}$ is the $d${\it th} Veronese subring of $R$. One of our results extends to arbitrary characteristic, in the case of rational monomial maps, a previous syzygy-theoretic birationality criterion in characteristic zero

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Aron Simis, Rafael H. Villarreal. 2006-01-09. Linear syzygies and birational combinatorics. https://arxiv.org/abs/math/0505159

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