Toward the classification of higher-dimensional toric Fano varieties

The purpose of this paper is to give basic tools for the classification of nonsingular toric Fano varieties by means of the notions of primitive collections and primitive relations due to Batyrev. By using them we can easily deal with equivariant blow-ups and blow-downs, and get an easy criterion to determine whether a given nonsingular toric variety is a Fano variety or not. As applications of these results, we get a toric version of a theorem of Mori, and can classify, in principle, all nonsingular toric Fano varieties obtained from a given nonsingular toric Fano variety by finite successions of equivariant blow-ups and blow-downs through nonsingular toric Fano varieties. Especially, we get a new method for the classification of nonsingular toric Fano varieties of dimension at most four. These methods are extended to the case of Gorenstein toric Fano varieties endowed with natural resolutions of singularities. Especially, we easily get a new method for the classification of Gorenstein toric Fano surfaces.Comment: 36 pages, Latex2e, to appear in Tohoku Math.

Growth of Villages in China, 1990-2002

This paper examines the economic and noneconomic determinants of growth disparity among Chinese villages between 1990 and 2002. By estimating a growth equation, first, we confirm a significant positive effect of the initial level of human capital, as well as the initial condition of physical infrastructure. Second, social capital measured by the degree of stable social relations at the village level is also a significant growth-promoting factor. The policy implications of our findings are that public policy promoting social stability in rural areas should be strengthened, as well as increasing financial support for rural education and infrastructure construction, especially in lower income regions.regional disparity, growth regression, social capital, rural China