Linear syzygies and birational combinatorics

Research paper by Aron Simis, Rafael H. Villarreal

Indexed on: 25 Apr '13Published on: 25 Apr '13Published in: Results in Mathematics


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 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].