Lectures On Riemann Surfaces - Proceedings Of The College On Riemann Surfaces
Author: Maurizio Cornalba
Publisher: World Scientific
Published: 1989-06-01
Total Pages: 716
ISBN-13: 9814590878
DOWNLOAD EBOOKPosts
Algebraic Curves and Riemann Surfaces
Author: Rick Miranda
Publisher: American Mathematical Soc.
Published: 1995
Total Pages: 414
ISBN-13: 0821802682
DOWNLOAD EBOOKIn this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.
Lectures on Riemann Surfaces
Author: Maurizio Cornalba
Publisher:
Published: 1989
Total Pages: 0
ISBN-13: 9789814503365
DOWNLOAD EBOOKThe first College on Riemann Surfaces centered on the theory of Riemann surfaces and their moduli and its applications to physics. This volume contains revised versions of the notes distributed at the College.
Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration
Author: Alfonso Zamora Saiz
Publisher: Springer Nature
Published: 2021-03-24
Total Pages: 127
ISBN-13: 3030678296
DOWNLOAD EBOOKThis book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.
Dirichlet Forms
Author: E. Fabes
Publisher: Springer
Published: 2006-11-15
Total Pages: 254
ISBN-13: 3540481516
DOWNLOAD EBOOKThe theory of Dirichlet forms has witnessed recently some very important developments both in theoretical foundations and in applications (stochasticprocesses, quantum field theory, composite materials,...). It was therefore felt timely to have on this subject a CIME school, in which leading experts in the field would present both the basic foundations of the theory and some of the recent applications. The six courses covered the basic theory and applications to: - Stochastic processes and potential theory (M. Fukushima and M. Roeckner) - Regularity problems for solutions to elliptic equations in general domains (E. Fabes and C. Kenig) - Hypercontractivity of semigroups, logarithmic Sobolev inequalities and relation to statistical mechanics (L. Gross and D. Stroock). The School had a constant and active participation of young researchers, both from Italy and abroad.
The Art of Doing Algebraic Geometry
Author: Thomas Dedieu
Publisher: Springer Nature
Published: 2023-04-14
Total Pages: 421
ISBN-13: 303111938X
DOWNLOAD EBOOKThis volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state of the art of the covered topics and reflecting the versatility of the scientific interests of Ciro Ciliberto.
Discontinuous Groups and Riemann Surfaces (AM-79), Volume 79
Author: Leon Greenberg
Publisher: Princeton University Press
Published: 2016-03-02
Total Pages: 452
ISBN-13: 1400881641
DOWNLOAD EBOOKStudy 79 contains a collection of papers presented at the Conference on Discontinuous Groups and Ricmann Surfaces at the University of Maryland, May 21-25, 1973. The papers, by leading authorities, deal mainly with Fuchsian and Kleinian groups, Teichmüller spaces, Jacobian varieties, and quasiconformal mappings. These topics are intertwined, representing a common meeting of algebra, geometry, and analysis.
Topics in the Theory of Riemann Surfaces
Author: Robert D.M. Accola
Publisher: Springer
Published: 2006-11-14
Total Pages: 117
ISBN-13: 3540490566
DOWNLOAD EBOOKThe book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. The extremely useful inequality of Castelnuovo- Severi is also treated. While the methods are elementary, much of the material does not appear in the current texts on Riemann surfaces, algebraic curves. The book is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.
Several Complex Variables. Maryland 1970. Proceedings of the International Mathematical Conference, Held at College Park, April 6-17, 1970
Author: John Horvath
Publisher: Springer
Published: 2006-11-15
Total Pages: 297
ISBN-13: 3540364935
DOWNLOAD EBOOKQuasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces
Author: Yunping Jiang
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 386
ISBN-13: 0821853406
DOWNLOAD EBOOKThis volume contains the proceedings of the AMS Special Session on Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces, held in honor of Clifford J. Earle, from October 2-3, 2010, in Syracuse, New York. This volume includes a wide range of papers on Teichmuller theory and related areas. It provides a broad survey of the present state of research and the applications of quasiconformal mappings, Riemann surfaces, complex dynamical systems, Teichmuller theory, and geometric function theory. The papers in this volume reflect the directions of research in different aspects of these fields and also give the reader an idea of how Teichmuller theory intersects with other areas of mathematics.
