Transcendental Methods in Algebraic Geometry
Author: Jean-Pierre Demailly
Publisher: Springer
Published: 2006-11-14
Total Pages: 266
ISBN-13: 3540496327
DOWNLOAD EBOOK →Author: Jean-Pierre Demailly
Publisher: Springer
Published: 2006-11-14
Total Pages: 266
ISBN-13: 3540496327
DOWNLOAD EBOOK →Author: Jean-Pierre Demailly
Publisher: Springer
Published: 1996-12-13
Total Pages: 0
ISBN-13: 9783540620389
DOWNLOAD EBOOK →Author: Robin Hartshorne
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 511
ISBN-13: 1475738498
DOWNLOAD EBOOK →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.
Author: Phillip A. Griffiths
Publisher: Princeton University Press
Published: 2016-03-02
Total Pages: 328
ISBN-13: 140088165X
DOWNLOAD EBOOK →The description for this book, Topics in Transcendental Algebraic Geometry. (AM-106), Volume 106, will be forthcoming.
Author: Jean-Pierre Demailly
Publisher:
Published: 2010
Total Pages: 231
ISBN-13: 9787040305319
DOWNLOAD EBOOK →Author: B. Brent Gordon
Publisher: Springer Science & Business Media
Published: 2000-02-29
Total Pages: 652
ISBN-13: 9780792361947
DOWNLOAD EBOOK →The subject of algebraic cycles has thrived through its interaction with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to such developments as a description of Chow groups in terms of algebraic K-theory, the arithmetic Abel-Jacobi mapping, progress on the celebrated conjectures of Hodge and Tate, and the conjectures of Bloch and Beilinson. The immense recent progress in algebraic cycles, based on so many interactions with so many other areas of mathematics, has contributed to a considerable degree of inaccessibility, especially for graduate students. Even specialists in one approach to algebraic cycles may not understand other approaches well. This book offers students and specialists alike a broad perspective of algebraic cycles, presented from several viewpoints, including arithmetic, transcendental, topological, motives and K-theory methods. Topics include a discussion of the arithmetic Abel-Jacobi mapping, higher Abel-Jacobi regulator maps, polylogarithms and L-series, candidate Bloch-Beilinson filtrations, applications of Chern-Simons invariants to algebraic cycles via the study of algebraic vector bundles with algebraic connection, motivic cohomology, Chow groups of singular varieties, and recent progress on the Hodge and Tate conjectures for Abelian varieties.
Author: Mark L. Green
Publisher: Springer
Published: 2004-09-02
Total Pages: 281
ISBN-13: 3540490469
DOWNLOAD EBOOK →The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.
Author: Viktor Blasjo
Publisher: Academic Press
Published: 2017-04-22
Total Pages: 284
ISBN-13: 0128132981
DOWNLOAD EBOOK →Transcendental Curves in the Leibnizian Calculus analyzes a mathematical and philosophical conflict between classical and early modern mathematics. In the late 17th century, mathematics was at the brink of an identity crisis. For millennia, mathematical meaning and ontology had been anchored in geometrical constructions, as epitomized by Euclid's ruler and compass. As late as 1637, Descartes had placed himself squarely in this tradition when he justified his new technique of identifying curves with equations by means of certain curve-tracing instruments, thereby bringing together the ancient constructive tradition and modern algebraic methods in a satisfying marriage. But rapid advances in the new fields of infinitesimal calculus and mathematical mechanics soon ruined his grand synthesis. Descartes's scheme left out transcendental curves, i.e. curves with no polynomial equation, but in the course of these subsequent developments such curves emerged as indispensable. It was becoming harder and harder to juggle cutting-edge mathematics and ancient conceptions of its foundations at the same time, yet leading mathematicians, such as Leibniz felt compelled to do precisely this. The new mathematics fit more naturally an analytical conception of curves than a construction-based one, yet no one wanted to betray the latter, as this was seen as virtually tantamount to stop doing mathematics altogether. The credibility and authority of mathematics depended on it. Brings to light this underlying and often implicit complex of concerns that permeate early calculus Evaluates the technical conception and mathematical construction of the geometrical method Reveals a previously unrecognized Liebnizian programmatic cohesion in early calculus Provides a beautifully written work of outstanding original scholarship
Author: Yuri V. Nesterenko
Publisher: Springer
Published: 2003-07-01
Total Pages: 257
ISBN-13: 3540445501
DOWNLOAD EBOOK →In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.