This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, K hler geometry, and group actions to Hodge theory and characteristic p-geometry.

Written by established experts this book will be a must for mathematicians working in Complex Geometry

The rapid development and expansion of Web-based technologies has vast potential implications for the processes of teaching and learning world-wide. Technological advancements of Web-based applications strike at the base of the education spectrum; however, the scope of experimentation and discussion on this topic has continuously been narrow.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Although sponges are one of the major components of littoral ecosystems, their systematics obviously lags behind that of the majority of other groups of marine invertebrates. Also the evolutionary trends in these most primitive of the Metazoans are poorly understood. The confused state of their taxonomy and the difficulties with their identification prevent their use in ecological studies. The emphasis of interest presently seems to have shifted towards chemistry, but many of the hundreds of interesting chemicals recently described in sponges pro bably have been found in mistakenly or imprecisely identified animals. This situ ation will become worse in the next few years, when a number of experts will retire and will not be replaced by new ones, owing to the difficulties that the science of systematics is facing in most countries - as exemplified during this meeting by an informal discussion on the endangered future of European Museums. Under these circumstances, it is the responsability of present sponge taxono mists to leave a less confused state and tools such as simple fauna or computerized data bases to generations following. These tools do not exist even in one of the best studied areas, the North-Eastern Atlantic (including the Mediterranean Sea).

This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, K hler geometry, and group actions to Hodge theory and characteristic p-geometry.

Written by established experts this book will be a must for mathematicians working in Complex Geometry

Introduction M. Kodaira's vanishing theorem, saying that the inverse of an ample invert ible sheaf on a projective complex manifold X has no cohomology below the dimension of X and its generalization, due to Y. Akizuki and S. Nakano, have been proven originally by methods from differential geometry ([39J and [1]). Even if, due to J.P. Serre's GAGA-theorems [56J and base change for field extensions the algebraic analogue was obtained for projective manifolds over a field k of characteristic p = 0, for a long time no algebraic proof was known and no generalization to p > 0, except for certain lower dimensional manifolds. Worse, counterexamples due to M. Raynaud [52J showed that in characteristic p > 0 some additional assumptions were needed. This was the state of the art until P. Deligne and 1. Illusie [12J proved the degeneration of the Hodge to de Rham spectral sequence for projective manifolds X defined over a field k of characteristic p > 0 and liftable to the second Witt vectors W2(k). Standard degeneration arguments allow to deduce the degeneration of the Hodge to de Rham spectral sequence in characteristic zero, as well, a re sult which again could only be obtained by analytic and differential geometric methods beforehand. As a corollary of their methods M. Raynaud (loc. cit.) gave an easy proof of Kodaira vanishing in all characteristics, provided that X lifts to W2(k).

The topological fundamental group of a smooth complex algebraic variety is poorly understood. One way to approach it is to consider its complex linear representations modulo conjugation, that is, its complex local systems. A fundamental problem is then to single out the complex points of such moduli spaces which correspond to geometric systems, and more generally to identify geometric subloci of the moduli space of local systems with special arithmetic properties. Deep conjectures have been made in relation to these problems. This book studies some consequences of these conjectures, notably density, integrality and crystallinity properties of some special loci. This monograph provides a unique compelling and concise overview of an active area of research and is useful to students looking to get into this area. It is of interest to a wide range of researchers and is a useful reference for newcomers and experts alike.

Title: Recherches sur Change -le s-Laval, par L. M. F. G. Completed by J. Guiller and G. Esnault.] tom. 2.Publisher: British Library, Historical Print EditionsThe British Library is the national library of the United Kingdom. It is one of the world's largest research libraries holding over 150 million items in all known languages and formats: books, journals, newspapers, sound recordings, patents, maps, stamps, prints and much more. Its collections include around 14 million books, along with substantial additional collections of manuscripts and historical items dating back as far as 300 BC.The GEOGRAPHY & TOPOGRAPHY collection includes books from the British Library digitised by Microsoft. Offering some insights into the study and mapping of the natural world, this collection includes texts on Babylon, the geographies of China, and the medieval Islamic world. Also included are regional geographies and volumes on environmental determinism, topographical analyses of England, China, ancient Jerusalem, and significant tracts of North America. ++++The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to insure edition identification: ++++ British Library Guiller, Louis Marie Franc ois; Esnault, Gustave Rene; Guiller, Joseph; 1882, 83. 8 . 10167.dd.7.

This Book Is In French. Due to the very old age and scarcity of this book, many of the pages may be hard to read due to the blurring of the original text.

This Book Is In French. Due to the very old age and scarcity of this book, many of the pages may be hard to read due to the blurring of the original text.