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Principles of Complex Analysis
This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they are really indispensable. This approach provides a motivation for the reader to digest more abstract definitions (e.g., those of sheaves or line bundles, which are not mentioned in the book) when he/she is ready for that level of abstraction indeed. In the chapter on Riemann surfaces, several key results on compact Riemann surfaces are stated and proved in the first nontrivial case, i.e. that of elliptic curves.
Serge Diaghïlev
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Serge Spitzer
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Algebraic Curves
This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford...
Serge Poliakoff
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Serge Poliakoff. Catalogue Raisonné. Vol
French painter born in Moscow (1900-1969). He left Russia in 1917 and arrived in Paris six years later. He studied at the Académie de la Grande Chaumière in Paris, then in London before meeting Delaunay and Kandinsky. He painted his first non-figurative works in 1938, yet only after the War did he truly mark out his own artistic domain. By progessively working his overlaid colors and irregular, imbricated forms, at once distinct and resonant with their own vibrations, he invested the canvas with the autonomy that operates out of strictly plastic necessity. He was quickly recognized as a major figure in the Abstract art to come out of the School of Paris, having staked out a very unique style that kept its distance from the overly rigid and cold precision of strict geometry, as much as it did from an overly gestural improvisation.
Serge Comte : z
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Real and Functional Analysis
This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
The Red Book of Varieties and Schemes
Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.
