Algebraic Curves The Brill And Noether Way
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Algebraic Curves The Brill And Noether Way
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Author : Eduardo Casas-Alvero
language : en
Publisher: Springer Nature
Release Date : 2019-11-30
Algebraic Curves The Brill And Noether Way written by Eduardo Casas-Alvero and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-30 with Mathematics categories.
The book presents the central facts of the local, projective and intrinsic theories of complex algebraic plane curves, with complete proofs and starting from low-level prerequisites. It includes Puiseux series, branches, intersection multiplicity, Bézout theorem, rational functions, Riemann-Roch theorem and rational maps. It is aimed at graduate and advanced undergraduate students, and also at anyone interested in algebraic curves or in an introduction to algebraic geometry via curves.
Geometry Of Algebraic Curves
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Author : Enrico Arbarello
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Geometry Of Algebraic Curves written by Enrico Arbarello and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
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).
The Practice Of Algebraic Curves
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Author : David Eisenbud
language : en
Publisher: American Mathematical Society
Release Date : 2024-11-09
The Practice Of Algebraic Curves written by David Eisenbud and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-09 with Mathematics categories.
This textbook provides readers with a working knowledge of the modern theory of complex projective algebraic curves. Also known as compact Riemann surfaces, such curves shaped the development of algebraic geometry itself, making this theory essential background for anyone working in or using this discipline. Examples underpin the presentation throughout, illustrating techniques that range across classical geometric theory, modern commutative algebra, and moduli theory. The book begins with two chapters covering basic ideas, including maps to projective space, invertible sheaves, and the Riemann?Roch theorem. Subsequent chapters alternate between a detailed study of curves up to genus six and more advanced topics such as Jacobians, Hilbert schemes, moduli spaces of curves, Severi varieties, dualizing sheaves, and linkage of curves in 3-space. Three chapters treat the refinements of the Brill?Noether theorem, including applications and a complete proof of the basic result. Two chapters on free resolutions, rational normal scrolls, and canonical curves build context for Green?s conjecture. The book culminates in a study of Hilbert schemes of curves through examples. A historical appendix by Jeremy Gray captures the early development of the theory of algebraic curves. Exercises, illustrations, and open problems accompany the text throughout. The Practice of Algebraic Curves offers a masterclass in theory that has become essential in areas ranging from algebraic geometry itself to mathematical physics and other applications. Suitable for students and researchers alike, the text bridges the gap from a first course in algebraic geometry to advanced literature and active research.
Geometry Of Algebraic Curves
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Author : Enrico Arbarello
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-10
Geometry Of Algebraic Curves written by Enrico Arbarello and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-10 with Mathematics categories.
The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source. The first volume appeared 1985 as vol. 267 of the same series.
From Classical To Modern Algebraic Geometry
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Author : Gianfranco Casnati
language : en
Publisher: Birkhäuser
Release Date : 2017-04-20
From Classical To Modern Algebraic Geometry written by Gianfranco Casnati and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-20 with Mathematics categories.
This book commemorates the 150th birthday of Corrado Segre, one of the founders of the Italian School of Algebraic Geometry and a crucial figure in the history of Algebraic Geometry. It is the outcome of a conference held in Turin, Italy. One of the book's most unique features is the inclusion of a previously unpublished manuscript by Corrado Segre, together with a scientific commentary. Representing a prelude to Segre's seminal 1894 contribution on the theory of algebraic curves, this manuscript and other important archival sources included in the essays shed new light on the eminent role he played at the international level. Including both survey articles and original research papers, the book is divided into three parts: section one focuses on the implications of Segre's work in a historic light, while section two presents new results in his field, namely Algebraic Geometry. The third part features Segre's unpublished notebook: Sulla Geometria Sugli Enti Algebrici Semplicemente Infiniti (1890-1891). This volume will appeal to scholars in the History of Mathematics, as well as to researchers in the current subfields of Algebraic Geometry.
The Richness Of The History Of Mathematics
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Author : Karine Chemla
language : en
Publisher: Springer Nature
Release Date : 2023-11-27
The Richness Of The History Of Mathematics written by Karine Chemla and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-27 with Mathematics categories.
This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the “what, why and how” of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the “how” question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.
The Way It Was
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Author : Donald Saari
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
The Way It Was written by Donald Saari and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
The formative years of the American Mathematical Society coincided with a time of remarkable development in mathematics. During this period, the Bulletin of the American Mathematical Society and its predecessor, The Bulletin of the New York Mathematical Society, served as a primary vehicle for reporting mathematics to American mathematicians. As a result, some of the most important and fundamental work of early twentieth-century mathematics found its way into the Bulletin. Milestone articles include Hilbert's problems presented at the 1900 Paris International Congress of Mathematicians (ICM), Poincare's 1904 lecture on the future of mathematical physics (with commentary suggesting that he was tantalizingly close to capturing the notion of relativity), and Klein's Erlangen program; all of these articles received added publicity when the first English translation was published in the Bulletin. This book reproduces these and other well-written articles from the early Bulletin, offering readers the best way to experience a slice of that time. Other articles in the book include, in particular, a report to American mathematicians about what happened at that important 1900 ICM meeting and three articles from the scientific portion of the 1904 centennial celebration of the Louisiana Purchase: Darboux describing the development of geometry, Pierpont focusing on nineteenth-century mathematics, and Poincare emphasizing the significance of mathematical physics. Accompanying the transition from the nineteenth to twentieth century was that new important thing called ``mathematical rigor''. Included is an article by Klein reflecting the beliefs of the time with his promotion of rigor. These are just some of the many topics characterizing the early days of the developing American mathematical community. The book offers a captivating review of mathematics through the early years of the Bulletin.
Geometry Of Algebraic Curves
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Author : E. Arbarello
language : en
Publisher: Springer Science & Business Media
Release Date : 1985
Geometry Of Algebraic Curves written by E. Arbarello and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
This comprehensive and self-contained account of the extrinsic geometry of algebraic curves applies the theory of linear series to a number of classical topics, including the geometry of the Reimann theta divisor, as well as to contemporary research.
Selected Works Of Phillip A Griffiths With Commentary
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Author : Phillip Griffiths
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Selected Works Of Phillip A Griffiths With Commentary written by Phillip Griffiths and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Containing four parts such as Analytic Geometry, Algebraic Geometry, Variations of Hodge Structures, and Differential Systems that are organized according to the subject matter, this title provides the reader with a panoramic view of important and exciting mathematics during the second half of the 20th century.
3264 And All That
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Author : David Eisenbud
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-14
3264 And All That written by David Eisenbud and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-14 with Mathematics categories.
3264, the mathematical solution to a question concerning geometric figures.