Rigid Geometry of Curves and Their Jacobians - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Rigid Geometry of Curves and Their Jacobians write by Werner Lütkebohmert. This book was released on 2016-01-26. Rigid Geometry of Curves and Their Jacobians available in PDF, EPUB and Kindle. This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
Curves and Their Jacobians
Curves and Their Jacobians - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Curves and Their Jacobians write by David Mumford. This book was released on 1975. Curves and Their Jacobians available in PDF, EPUB and Kindle.
Rigid Analytic Curves and Their Jacobians
Rigid Analytic Curves and Their Jacobians - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Rigid Analytic Curves and Their Jacobians write by Sophie Schmieg. This book was released on 2013. Rigid Analytic Curves and Their Jacobians available in PDF, EPUB and Kindle.
Geometry of Curves
Geometry of Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry of Curves write by J.W. Rutter. This book was released on 2018-10-03. Geometry of Curves available in PDF, EPUB and Kindle. Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, we need to offer students an introduction with modest prerequisites, one that stimulates their interest and focuses on problem solving. Integrating parametric, algebraic, and projective curves into a single text, Geometry of Curves offers students a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. The author begins with the basics, then takes students on a fascinating journey from conics, higher algebraic and transcendental curves, through the properties of parametric curves, the classification of limaçons, envelopes, and finally to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness. The uniqueness of this treatment lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations. The result is a practical text, almost entirely self-contained, that not only imparts a deeper understanding of the theory, but inspires a heightened appreciation of geometry and interest in more advanced studies.
Geometry of Algebraic Curves
Geometry of Algebraic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry of Algebraic Curves write by Enrico Arbarello. This book was released on 2013-11-11. Geometry of Algebraic Curves available in PDF, EPUB and Kindle. In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 1950's and 1960's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory. It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre sents a significant advance beyond the legacy left by the classical geometers such as Noether, Castelnuovo, Enriques, and Severi. These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Along the way we shall, of course, discuss appli cations of the theory of linear series to a number of classical topics (e.g., the geometry of the Riemann theta divisor) as well as to some of the current research (e.g., the Kodaira dimension of the moduli space of curves).
