On K\"ahler conformal compactifications of U(n)U(n)-invariant ALE spaces

We prove that a certain class of ALE spaces always has a Kahler conformal compactification, and moreover provide explicit formulas for the conformal factor and the Kahler potential of said compactification. We then apply this to give a new and simple construction of the canonical Bochner-K\"ahler metric on certain weighted projective spaces, and also to explicitly construct a family Kahler edge-cone metrics on $\mathbb{CP}^2$, with singular set $\mathbb{CP}^1$, having cone angles $2\pi\beta$ for all $\beta>0$. We conclude by discussing how these results can be used to obtain certain well-known Einstein metrics.Comment: 14 page

Entrepreneurship and Economic Growth: An Investigation into the Relationship between Entrepreneurship and Total Factor Productivity Growth in the EU

Endogenous growth theory assigns an important role for entrepreneurship in the process of economic development. This paper sets to formally test the impact of entrepreneurship on economic growth. Entrepreneurship is represented by a number of proxy variables, whereas Total Factor Productivity is used as a measure of economic growth. Panel data of 26 European countries repeatedly sampled over a period of 11 years is used to estimate a Random Effects model. This study finds that entrepreneurship contributes to growth moderately. It is not, nonetheless, a dominant force shaping changes in TFP growth rates. Business Birth Rate, Self-employment Rate, Business Investment and Labour Productivity Growth were all found to be highly significant. The article concludes that more encompassing measure of entrepreneurship needs to be developed, one that would reflect the complexity of the notion.entrepreneurship, total factor productivity, economic growth, the EU