Details:
Title  Toric ideals for high Veronese subrings of toric algebras.  Author(s)  Takafumi Shibuta  Type  Article in Journal  Abstract  We prove that the defining ideal of a sufficiently high Veronese subring of a toric algebra admits a quadratic Gröbner basis consisting of binomials. More generally, we prove that the defining ideal of a sufficiently high Veronese subring of a standard graded ring admits a quadratic Gröbner basis. We give a lower bound on d such that the defining ideal of dth Veronese subring admits a quadratic Gröbner basis. Eisenbud–Reeves–Totaro stated the same theorem without a proof with some lower bound on d. In many cases, our lower bound is less than Eisenbud–Reeves–Totaro’s lower bound.  ISSN  00192082 
URL 
http://projecteuclid.org/euclid.ijm/1369841790 
Language  English  Journal  Ill. J. Math.  Volume  55  Number  3  Pages  895905  Publisher  University of Illinois, Department of Mathematics, Urbana, IL  Year  2011  Edition  0  Translation 
No  Refereed 
No 
