1.1. TROPICAL HYPERSURFACES 9 0 1 0 Figure 9. The Newton polytope and subdivision for Figure 2. 0 0 5 1 0 5 Figure 10. The Newton polytope and subdivision for Figure 3. 0 0 9 3 0 1 Figure 11. The Newton polytope and subdivision for Figure 4. This description of V (f) leads to an important condition known as the balancing condition. Specifically, for each ˇ ∈ ˇ[n−2], a codimension two cell, let ˇ1,..., ˇk ∈ ˇ[n−1] be the cells containing it in V (f), with weights w1,...,wk. Note that ω is a two-dimensional cell of P and τ1,...,τk are the edges of ω. Let n1,...,nk ∈ N be primitive tangent vectors to τ1,...,τk, pointing in directions consistent with the orientations on τ1,...,τk induced by some chosen orientation on ω. The vectors n1,...,nk are primitive normal vectors to ˇ1,..., ˇk. Indeed, the endpoints of τi

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2011 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.