Abelian varieties are a natural generalization of elliptic curves to higher dimensions, whose geometry and classification are as rich in elegant results as in the one-dimensional ease. The use of theta functions, particularly since Mumford's work, has been an important tool in the study of abelian varieties and invertible sheaves on them. Also, abelian varieties play a significant role in the geometric approach to modern algebraic number theory. In this book, Kempf has focused on the analytic aspects of the geometry of abelian varieties, rather than taking the alternative algebraic or arithmetic points of view. His purpose is to provide an introduction to complex analytic geometry. Thus, he uses Hermitian geometry as much as possible. One distinguishing feature of Kempf's presentation is the systematic use of Mumford's theta group. This allows him to give precise results about the projective ideal of an abelian variety. In its detailed discussion of the cohomology of invertible sheaves, the book incorporates material previously found only in research articles. Also, several examples where abelian varieties arise in various branches of geometry are given as a conclusion of the book.

Scholarly Research Paper from the year 2006 in the subject Economics - Case Scenarios, grade: 1,5, University of Cooperative Education Mannheim, course: International Seminar, language: English, abstract: This term paper on hand analyses the competitiveness of five African nations. Depending on the data from the WEF, five African nations have been chosen. These are in detail South Africa, Botswana, Namibia, Mauritius and Egypt. The main goal of this paper was to analyze these countries in their competitiveness and benchmark them as an example for other African nations. Therefore this paper first gives an overview on the current political situation, the geographical conditions and the historic background to each country. Each country then is analyzed in the primary, secondary and tertiary sector and gives details on the main economical challenges of each country. The benchmarking deals with the performance in different categories which are Government Efficiency, Business Efficiency, Economic Performance and Infrastructure. The paper on hand comes to the conclusion that the selected five countries are indeed very competitive countries within the African continent. They all have dealt with problematic fields of their economy in the past in their individual way and thus improved their performance. The majority of these five countries still have to work harder on these problematic areas to reach a worldwide competitive level, some of them have already reached this level to some extent. The necessary background information and statistics have been taken from the World Economic Forum (WEF) and various reliable internet resources. The paper on hand analyses the data within the past 16 years or more, depending on the question analysed.