From Classical To Modern Algebraic Geometry
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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 One of the book's most unique features is the inclusion of a previously unpublished manuscript by Corrado Segre, together with a scientific commentary.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 The third part features Segre's unpublished notebook: Sulla Geometria Sugli Enti Algebrici Semplicemente Infiniti (1890-1891).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.
Classical Algebraic Geometry
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Author : Igor V. Dolgachev
language : en
Publisher: Cambridge University Press
Release Date : 2012-08-16
Classical Algebraic Geometry written by Igor V. Dolgachev 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 2012-08-16 with Mathematics categories.
Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.
Classical Algebraic Geometry
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Author : Igor V. Dolgachev
language : en
Publisher:
Release Date : 2012
Classical Algebraic Geometry written by Igor V. Dolgachev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Geometry, Algebraic categories.
Classical Algebraic Geometry
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Author : Igor V. Dolgachev
language : en
Publisher:
Release Date : 2014-05-14
Classical Algebraic Geometry written by Igor V. Dolgachev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Geometry, Algebraic categories.
Makes classical algebraic geometry accessible to the modern mathematician.
Algebraic Curves
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Author : Maxim E. Kazaryan
language : en
Publisher: Springer
Release Date : 2019-01-21
Algebraic Curves written by Maxim E. Kazaryan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-21 with Mathematics categories.
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, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework
Algebraic Geometry
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Author : Solomon Lefschetz
language : en
Publisher: Princeton University Press
Release Date : 2015-12-08
Algebraic Geometry written by Solomon Lefschetz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.
The first application of modern algebraic techniques to a comprehensive selection of classical geometric problems. Written with spirit and originality, this is a valuable book for anyone interested in the subject from other than the purely algebraic point of view. Originally published in 1953. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Positivity In Algebraic Geometry I
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Author : R.K. Lazarsfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-08-24
Positivity In Algebraic Geometry I written by R.K. Lazarsfeld 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 2004-08-24 with History categories.
This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.
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.
An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Introduction To Algebraic Geometry
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Author : Steven Dale Cutkosky
language : en
Publisher:
Release Date : 2018
Introduction To Algebraic Geometry written by Steven Dale Cutkosky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Geometry, Algebraic categories.
This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic 0 and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More.
Advances In Algebraic Geometry Motivated By Physics
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Author : Emma Previato
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Advances In Algebraic Geometry Motivated By Physics written by Emma Previato 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 2001 with Mathematics categories.
Our knowledge of objects of algebraic geometry such as moduli of curves, (real) Schubert classes, fundamental groups of complements of hyperplane arrangements, toric varieties, and variation of Hodge structures, has been enhanced recently by ideas and constructions of quantum field theory, such as mirror symmetry, Gromov-Witten invariants, quantum cohomology, and gravitational descendants. These are some of the themes of this refereed collection of papers, which grew out of the special session, ``Enumerative Geometry in Physics,'' held at the AMS meeting in Lowell, MA, April 2000. This session brought together mathematicians and physicists who reported on the latest results and open questions; all the abstracts are included as an Appendix, and also included are papers by some who could not attend. The collection provides an overview of state-of-the-art tools, links that connect classical and modern problems, and the latest knowledge available.