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Download or read book Degenerating Curves and Their Jacobians written by Dino Jacques Lorenzini and published by . This book was released on 1988 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Werner Lütkebohmert
Publisher: Springer
Published: 2016-01-26
Total Pages: 398
ISBN-13: 331927371X
DOWNLOAD EBOOKThis book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
Download or read book Rigid Geometry of Curves and Their Jacobians written by Werner Lütkebohmert and published by Springer. This book was released on 2016-01-26 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
Author: David Mumford
Publisher: Ann Arbor : University of Michigan Press, c1975, 1976 printing.
Published: 1975
Total Pages: 120
ISBN-13:
DOWNLOAD EBOOKDownload or read book Curves and Their Jacobians written by David Mumford and published by Ann Arbor : University of Michigan Press, c1975, 1976 printing.. This book was released on 1975 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: A.N. Parshin
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 275
ISBN-13: 3662036622
DOWNLOAD EBOOKThis two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties. An excellent companion to the older classics on the subject.
Download or read book Algebraic Geometry III written by A.N. Parshin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties. An excellent companion to the older classics on the subject.
Download or read book Rigid Analytic Curves and Their Jacobians written by Sophie Schmieg and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Ron Donagi
Publisher: American Mathematical Soc.
Published: 1992
Total Pages: 354
ISBN-13: 0821851438
DOWNLOAD EBOOKThis volume contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on the Schottky Problem, held in June 1990 at the University of Massachusetts at Amherst. The conference explored various aspects of the Schottky problem of characterizing Jacobians of curves among all abelian varieties. Some of the articles study related themes, including the moduli of stable vector bundles on a curve. Prym varieties and intermediate Jacobians, and special Jacobians with exotic polarizations or product structures.
Download or read book Curves, Jacobians, and Abelian Varieties written by Ron Donagi and published by American Mathematical Soc.. This book was released on 1992 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on the Schottky Problem, held in June 1990 at the University of Massachusetts at Amherst. The conference explored various aspects of the Schottky problem of characterizing Jacobians of curves among all abelian varieties. Some of the articles study related themes, including the moduli of stable vector bundles on a curve. Prym varieties and intermediate Jacobians, and special Jacobians with exotic polarizations or product structures.
Author: Günter Harder
Publisher: Springer Science & Business Media
Published: 2011-04-21
Total Pages: 376
ISBN-13: 3834881597
DOWNLOAD EBOOKThis second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved. Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.
Download or read book Lectures on Algebraic Geometry II written by Günter Harder and published by Springer Science & Business Media. This book was released on 2011-04-21 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved. Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.
Download or read book Jacobians of Shimura Curves and Jacquet-Langlands Correspondences written by David Frederick Helm and published by . This book was released on 2003 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: David Mumford
Publisher: Springer
Published: 2004-02-21
Total Pages: 316
ISBN-13: 3540460217
DOWNLOAD EBOOKMumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.
Download or read book The Red Book of Varieties and Schemes written by David Mumford and published by Springer. This book was released on 2004-02-21 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.
Author: Valery Alexeev
Publisher: American Mathematical Soc.
Published: 2008
Total Pages: 290
ISBN-13: 0821843346
DOWNLOAD EBOOK"This book is devoted to recent progress in the study of curves and abelian varieties. It discusses both classical aspects of this deep and beautiful subject as well as two important new developments, tropical geometry and the theory of log schemes." "In addition to original research articles, this book contains three surveys devoted to singularities of theta divisors. of compactified Jucobiuns of singular curves, and of "strange duality" among moduli spaces of vector bundles on algebraic varieties."--BOOK JACKET.
Download or read book Curves and Abelian Varieties written by Valery Alexeev and published by American Mathematical Soc.. This book was released on 2008 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is devoted to recent progress in the study of curves and abelian varieties. It discusses both classical aspects of this deep and beautiful subject as well as two important new developments, tropical geometry and the theory of log schemes." "In addition to original research articles, this book contains three surveys devoted to singularities of theta divisors. of compactified Jucobiuns of singular curves, and of "strange duality" among moduli spaces of vector bundles on algebraic varieties."--BOOK JACKET.
