Degenerating Curves and Their Jacobians
Title | Degenerating Curves and Their Jacobians PDF eBook |
Author | Dino Jacques Lorenzini |
Publisher | |
Pages | 174 |
Release | 1988 |
Genre | |
ISBN |
Rigid Geometry of Curves and Their Jacobians
Title | Rigid Geometry of Curves and Their Jacobians PDF eBook |
Author | Werner Lütkebohmert |
Publisher | Springer |
Pages | 398 |
Release | 2016-01-26 |
Genre | Mathematics |
ISBN | 331927371X |
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.
Curves and Their Jacobians
Title | Curves and Their Jacobians PDF eBook |
Author | David Mumford |
Publisher | Ann Arbor : University of Michigan Press, c1975, 1976 printing. |
Pages | 120 |
Release | 1975 |
Genre | Mathematics |
ISBN |
Algebraic Geometry III
Title | Algebraic Geometry III PDF eBook |
Author | A.N. Parshin |
Publisher | Springer Science & Business Media |
Pages | 275 |
Release | 2013-04-17 |
Genre | Mathematics |
ISBN | 3662036622 |
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.
Curves, Jacobians, and Abelian Varieties
Title | Curves, Jacobians, and Abelian Varieties PDF eBook |
Author | Ron Donagi |
Publisher | American Mathematical Soc. |
Pages | 354 |
Release | 1992 |
Genre | Mathematics |
ISBN | 0821851438 |
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.
Rigid Analytic Curves and Their Jacobians
Title | Rigid Analytic Curves and Their Jacobians PDF eBook |
Author | Sophie Schmieg |
Publisher | |
Pages | |
Release | 2013 |
Genre | |
ISBN |
Lectures on Algebraic Geometry II
Title | Lectures on Algebraic Geometry II PDF eBook |
Author | Günter Harder |
Publisher | Springer Science & Business Media |
Pages | 376 |
Release | 2011-04-21 |
Genre | Mathematics |
ISBN | 3834881597 |
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.