Poset resolutions and lattice-linear monomial ideals

We introduce the class of lattice-linear monomial ideals and use the lcm-lattice to give an explicit construction for their minimal free resolution. The class of lattice-linear ideals includes (among others) the class of monomial ideals with a linear free resolution and the class of Scarf monomial ideals. Our main tool is a new construction by Tchernev that produces from a map of posets η:P→Nn a sequence of multigraded modules and maps.