Toric Varieties

In Part I we studied discriminants and resultants in the general context of projective geometry: our setup was that of an arbitrary projective variety X ⊂ Pn−1. We now want to move into a more combinatorial setting, which is closer to the classical concept of discriminants and resultants for polynomials. This setting corresponds to the situation when X ⊂ Pn−1 is a toric variety. In the present chapter, we have adapted the theory of toric varieties for our purposes. Since there are several references available on the subject [D] [Fu 2] [O], we did not attempt to be exhaustive or self-contained. Our exposition is organized “from the special to the general” so that the general description of toric varieties in terms of fans appears at the very end of the chapter.