Linear syzygies and birational combinatorics

الأصل · EN

Let F be a finite set of monomials of the same degree d≥ 2 in a polynomial ring R=k[x₁,...,xₙ] 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 d 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