Invariance of Plurigenera

The following conjecture on the deformation invariance of plurigenera is proved. For a smooth projective holomorphic family of compact complex manifolds over the open unit 1-disk such that all the fibers are of general type, every plurigenus of the fiber is independent of the fiber. The proof uses Nadel's multiplier ideal sheaves, Skoda's result on the generation of ideals with L2 estimates with respect to a plurisubharmonic weight, and the extension theorem of Ohsawa-Takegoshi-Manivel for holomorphic top-degree forms which are L2 with respect to a plurisubharmonic weight.Comment: 13 pages, LaTeX fil

The Direct Substitution Between Government and Private Consumption in East Asia

We investigate empirically the extent to which government consumption substitutes for private consumption in nine East Asia countries. Panel cointegrating regression uncovers a significantly positive elasticity of substitution between government and private consumption, implying on average government and private consumption are substitutes in East Asia. Country-by-country analysis, however, reveals diversity in the substitutability estimates. The four North East countries %u2013 China, Hong Kong, Japan, and Korea %u2013 tend to share similar and moderate values of the substitution elasticity. For the five ASEAN countries studied in this paper, the relationship between private and government consumption vary substantially, both in the sign and magnitude of the elasticity of substitution. Private and government consumption in Malaysia and Thailand are strong substitutes, but they are found to be complements in Indonesia and Singapore. In between is the Philippines which has a near zero elasticity of substitution.