PRODUCTS ON THE CHOW RINGS FOR TORIC VARIETIES

Toric variety is a normal algebraic variety containing algebraic torus $T_N$ as an open dense subset with an algebraic action of $T_N$ which is an extension of the group law of $T_N$. A toric variety can be described in terms of a certain collection, which is called a fan, of cones. From this fact, the properties of a toric variety have strong connection with the combinatorial structure of the corresponding fan and the relations among the generators. That is, we can translate the diffcult algebrogeometric properties of toric varieties into very simple properties about the combinatorics of cones in affine spaces over the reals.