Curves In Projective Space
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Curves In Projective Space
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Author : Joe Harris
language : en
Publisher: Montréal : Presses de l'Université de Montréal
Release Date : 1982-01-01
Curves In Projective Space written by Joe Harris and has been published by Montréal : Presses de l'Université de Montréal this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Courbes algébriques categories.
Geometry Of Curves
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Author : J.W. Rutter
language : en
Publisher: CRC Press
Release Date : 2018-10-03
Geometry Of Curves written by J.W. Rutter and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
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.
Plane Algebraic Curves
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Author : C. Orzech
language : en
Publisher: CRC Press
Release Date : 2024-12-11
Plane Algebraic Curves written by C. Orzech and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-11 with Mathematics categories.
This book introduces the contemporary notions of algebraic varieties, morphisms of varieties, and adeles to the classical subject of plane curves over algebraically closed fields. It is useful for advanced undergraduate and beginning graduate students in mathematics.
Lectures On Curves Surfaces And Projective Varieties
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Author : Mauro Beltrametti
language : en
Publisher: European Mathematical Society
Release Date : 2009
Lectures On Curves Surfaces And Projective Varieties written by Mauro Beltrametti and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.
Characteristic Numbers Of Genus One Space Curves
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Author : Dung Hoang Nguyen
language : en
Publisher: Stanford University
Release Date : 2011
Characteristic Numbers Of Genus One Space Curves written by Dung Hoang Nguyen and has been published by Stanford University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
The purpose of this thesis is to develop an algorithm to compute all the characteristic numbers of genus one curves in projective spaces of arbitrary dimension. The characteristic numbers of genus zero curves, genus zero curves with an ordinary node, genus zero curves with an ordinary cusp are also computed en route.
Geometric Theory Of Algebraic Space Curves
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Author : S.S. Abhyankar
language : en
Publisher: Springer
Release Date : 2006-11-15
Geometric Theory Of Algebraic Space Curves written by S.S. Abhyankar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Algebraic Geometry
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Author : Robin Hartshorne
language : en
Publisher: Springer Science & Business Media
Release Date : 1977-12-19
Algebraic Geometry written by Robin Hartshorne 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 1977-12-19 with Mathematics categories.
This book provides an introduction to abstract algebraic geometry. It includes more than 400 exercises that offer specific examples as well as more specialized topics. From the reviews: "Enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed currently to answer these questions." --MATHEMATICAL REVIEWS
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.
Space Curves
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Author : Franco Ghione
language : fr
Publisher: Springer
Release Date : 2006-11-15
Space Curves written by Franco Ghione and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The main topics of the conference on "Curves in Projective Space" were good and bad families of projective curves, postulation of projective space curves and classical problems in enumerative geometry.
Algebraic Curves And Their Applications
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Author : Lubjana Beshaj
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-02-26
Algebraic Curves And Their Applications written by Lubjana Beshaj 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 2019-02-26 with Mathematics categories.
This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more. Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography. This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics.