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Linear syzygies and birational combinatorics

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Abstract

Let F be a finite set of monomials of the same degree d ≥ 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] ⊂ R (d), where R (d) is the dth Veronese subring of R. One of our results extends to arbitrary characteristic, in the case of rational monomial maps, a previous syzygytheoretic birationality criterion in characteristic zero obtained in [1].

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Pernambuco, 50740-540, Recife, Pe, Brazil

    Aron Simis

  2. Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14-740, 07000, México City, D.F.

    Rafael H. Villarreal

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  1. Aron Simis
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  2. Rafael H. Villarreal
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Correspondence to Aron Simis.

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Simis, A., Villarreal, R.H. Linear syzygies and birational combinatorics. Results. Math. 48, 326–343 (2005). https://doi.org/10.1007/BF03323372

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