On the classification of toric Fano 4-folds (Q1296188)

The author proves that there are exactly 123 types of toric Fano varieties up to isomorphisms. In general, such classification is very complicated as already evident in the 3-dimensional case. So the paper is a big step in higher dimensional geometry. In toric language, such classification is equivalent to that of special simplicial polyhedra. In the recent preprint by \textit{H. Sato} [``Toward the classification of higher dimensional toric Fano varieties''; \url{http://front.math.ucdavis.edu/Math.AG/9911022}], Batyrev's method has been employed and applied to higher dimensional cases (one missing isomorphism class is also added).