Algebraic Geometry
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Algebraic Geometry For Scientists And Engineers
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Author : Shreeram Shankar Abhyankar
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Algebraic Geometry For Scientists And Engineers written by Shreeram Shankar Abhyankar 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 1990 with Mathematics categories.
Based on lectures presented in courses on algebraic geometry taught by the author at Purdue University, this book covers various topics in the theory of algebraic curves and surfaces, such as rational and polynomial parametrization, functions and differentials on a curve, branches and valuations, and resolution of singularities.
Algebraic Geometry
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Author : Robin Hartshorne
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
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 2013-06-29 with Mathematics categories.
Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he moved to California where he is now Professor at the University of California at Berkeley. He is the author of "Residues and Duality" (1966), "Foundations of Projective Geometry (1968), "Ample Subvarieties of Algebraic Varieties" (1970), and numerous research titles. His current research interest is the geometry of projective varieties and vector bundles. He has been a visiting professor at the College de France and at Kyoto University, where he gave lectures in French and in Japanese, respectively. Professor Hartshorne is married to Edie Churchill, educator and psychotherapist, and has two sons. He has travelled widely, speaks several foreign languages, and is an experienced mountain climber. He is also an accomplished amateur musician: he has played the flute for many years, and during his last visit to Kyoto he began studying the shakuhachi.
Algebraic Geometry
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Author : Ulrich Görtz
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-06
Algebraic Geometry written by Ulrich Görtz 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 2010-08-06 with Mathematics categories.
This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.
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
Algebraic Geometry Explained
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date :
Algebraic Geometry Explained written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Embark on a captivating journey through the world of algebraic geometry with this comprehensive and accessible guide. Delve into the intricate relationship between algebra and geometry, uncovering the hidden structures that govern the behavior of geometric objects. Discover the foundations of algebraic geometry, where we lay the groundwork for understanding algebraic varieties, the central objects of study in this field. Explore the concept of schemes, a generalized notion of space that extends the familiar concept of varieties, providing a powerful framework for studying geometric objects in great generality. Unravel the mysteries of curves, the simplest and most fundamental type of algebraic variety. Investigate their properties, classifications, and applications, uncovering their significance in diverse fields such as cryptography and error-correcting codes. Explore the realm of surfaces, two-dimensional varieties with rich geometric and topological structures. Discover quadrics, ruled and developable surfaces, and embark on a journey to classify these surfaces, revealing their unique characteristics and applications in architecture and engineering. Venture into the vast landscape of higher-dimensional varieties, where we uncover the intricate interplay between geometry and topology. Investigate intersections and cohomology, unveiling the topological secrets of varieties. Delve into the concept of divisors and linear systems, gaining insights into the behavior of algebraic varieties. Witness the power of algebraic geometry as we explore its diverse applications. Discover the connections between algebraic geometry and coding theory, cryptography, physics, and number theory, showcasing the remarkable versatility of this mathematical discipline. With clear explanations, engaging examples, and insightful connections to other areas of mathematics, this book is an essential resource for students, researchers, and anyone fascinated by the beauty and power of algebraic geometry. Immerse yourself in the world of algebraic geometry and uncover the hidden elegance that lies at the intersection of algebra and geometry. If you like this book, write a review!
Methods Of Algebraic Geometry
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Author : William Vallance Douglas Hodge
language : en
Publisher: CUP Archive
Release Date : 1947
Methods Of Algebraic Geometry written by William Vallance Douglas Hodge and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1947 with Abelian varieties categories.
This classic work, in three volumes, provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasized throughout.
History Algebraic Geometry
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Author : Jean Dieudonné
language : en
Publisher: CRC Press
Release Date : 1985-05-30
History Algebraic Geometry written by Jean Dieudonné and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-05-30 with Mathematics categories.
This book contains several fundamental ideas that are revived time after time in different guises, providing a better understanding of algebraic geometric phenomena. It shows how the field is enriched with loans from analysis and topology and from commutative algebra and homological algebra.
Algebraic Geometry I
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Author : David Mumford
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-02-15
Algebraic Geometry I written by David Mumford 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 1995-02-15 with Mathematics categories.
From the reviews: "Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's "Volume I" is, together with its predecessor the red book of varieties and schemes, now as before one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics!" Zentralblatt
Undergraduate Algebraic Geometry
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Author : Miles Reid
language : en
Publisher: Cambridge University Press
Release Date : 1988-12-15
Undergraduate Algebraic Geometry written by Miles Reid 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 1988-12-15 with Mathematics categories.
Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to the basic concepts of algebraic geometry including: plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. He is at pains to stress the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book arises from an undergraduate course given at the University of Warwick and contains numerous examples and exercises illustrating the theory.
Algebraic Geometry
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Author : Gerrit Hayson
language : en
Publisher:
Release Date :
Algebraic Geometry written by Gerrit Hayson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In the grand tapestry of mathematics, few subjects weave together abstract thought and visual intuition as elegantly as algebraic geometry. This field represents one of humanity's most ambitious intellectual achievements: the creation of a bridge between the symbolic world of algebra and the spatial realm of geometry. To understand algebraic geometry is to witness the profound unity that underlies seemingly disparate mathematical concepts. The journey begins with a simple yet revolutionary idea. Every polynomial equation corresponds to a geometric shape, and conversely, every geometric shape can be described through algebraic equations. Consider the humble equation x² + y² = 1. To an algebraist, this represents a relationship between variables, a constraint that solutions must satisfy. To a geometer, it describes a perfect circle centered at the origin with radius one. Algebraic geometry recognizes that these are not two different mathematical objects but rather two perspectives on the same fundamental entity. This duality extends far beyond simple circles. The equation y = x² defines a parabola, while y² = x³ describes a cubic curve with a distinctive cusp. More complex polynomial equations generate increasingly intricate curves and surfaces, each possessing both algebraic properties derived from the equations and geometric properties visible to the eye. The genius of algebraic geometry lies in its ability to translate problems from one domain to the other, using whichever approach offers the clearest path to understanding.