Scarf lattice ideals

Abstract

This paper deals with the Scarf property of lattice ideals initiated by Peeva and Sturmfels[10], [11]. We will present a Scarf lattice ideal that is neither generic nor of codimension 2 and show that this property gives rise to several algebraic and combinatorial properties. In particular, we prove that for monomial curves, this property coincides with the notion of genericity, and that certain Scarf lattice ideals can have certain Scarf initial ideals.