Differential Forms On Singular Varieties PDF Download
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Author | : Vincenzo Ancona |
Publisher | : CRC Press |
Total Pages | : 312 |
Release | : 2005-08-24 |
Genre | : Mathematics |
ISBN | : 1420026526 |
Download Differential Forms on Singular Varieties Book in PDF, ePub and Kindle
Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of hig
Author | : Maks A. Akivis |
Publisher | : Springer Science & Business Media |
Total Pages | : 272 |
Release | : 2006-04-18 |
Genre | : Mathematics |
ISBN | : 0387215115 |
Download Differential Geometry of Varieties with Degenerate Gauss Maps Book in PDF, ePub and Kindle
This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.
Author | : Gerd Fischer |
Publisher | : Springer Science & Business Media |
Total Pages | : 153 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3322802175 |
Download Ruled Varieties Book in PDF, ePub and Kindle
Ruled varieties are unions of a family of linear spaces. They are objects of algebraic geometry as well as differential geometry, especially if the ruling is developable. This book is an introduction to both aspects, the algebraic and differential one. Starting from very elementary facts, the necessary techniques are developed, especially concerning Grassmannians and fundamental forms in a version suitable for complex projective algebraic geometry. Finally, this leads to recent results on the classification of developable ruled varieties and facts about tangent and secant varieties. Compared to many other topics of algebraic geometry, this is an area easily accessible to a graduate course.
Author | : Jędrzej Śniatycki |
Publisher | : Cambridge University Press |
Total Pages | : 249 |
Release | : 2013-06-13 |
Genre | : Mathematics |
ISBN | : 1107022711 |
Download Differential Geometry of Singular Spaces and Reduction of Symmetry Book in PDF, ePub and Kindle
A complete presentation of the theory of differential spaces, with applications to the study of singularities in systems with symmetry.
Author | : Shigeyuki Morita |
Publisher | : American Mathematical Soc. |
Total Pages | : 356 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 9780821810453 |
Download Geometry of Differential Forms Book in PDF, ePub and Kindle
Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms. The book by Morita is a comprehensive introduction to differential forms. It begins with a quick introduction to the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results concerning them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated is a detailed description of the Chern-Weil theory. The book can serve as a textbook for undergraduate students and for graduate students in geometry.
Author | : Ernst Kunz |
Publisher | : American Mathematical Soc. |
Total Pages | : 177 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821847600 |
Download Residues and Duality for Projective Algebraic Varieties Book in PDF, ePub and Kindle
"This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of (possibly singular) algebraic varieties over algebraically closed base fields. It describes duality and residue theorems in terms of Kahler differential forms and their residues. The properties of residues are introduced via local cohomology. Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations." "The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership, D. A. Cox explains toric residues and relates them to the earlier text." "The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given."--BOOK JACKET.
Author | : Jean-Paul Brasselet |
Publisher | : Springer |
Total Pages | : 242 |
Release | : 2009-11-28 |
Genre | : Mathematics |
ISBN | : 3642052053 |
Download Vector fields on Singular Varieties Book in PDF, ePub and Kindle
Many authors have questioned the use of the index of the vector field, and of the Chern classes, if the underlying space becomes singular. This book discusses their explorations within the framework of the obstruction theory and the Chern-Weil theory.
Author | : Manfredo P. Do Carmo |
Publisher | : Springer Science & Business Media |
Total Pages | : 124 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642579515 |
Download Differential Forms and Applications Book in PDF, ePub and Kindle
An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.
Author | : Tadao Oda |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2012-02-23 |
Genre | : Mathematics |
ISBN | : 9783642725494 |
Download Convex Bodies and Algebraic Geometry Book in PDF, ePub and Kindle
The theory of toric varieties (also called torus embeddings) describes a fascinating interplay between algebraic geometry and the geometry of convex figures in real affine spaces. This book is a unified up-to-date survey of the various results and interesting applications found since toric varieties were introduced in the early 1970's. It is an updated and corrected English edition of the author's book in Japanese published by Kinokuniya, Tokyo in 1985. Toric varieties are here treated as complex analytic spaces. Without assuming much prior knowledge of algebraic geometry, the author shows how elementary convex figures give rise to interesting complex analytic spaces. Easily visualized convex geometry is then used to describe algebraic geometry for these spaces, such as line bundles, projectivity, automorphism groups, birational transformations, differential forms and Mori's theory. Hence this book might serve as an accessible introduction to current algebraic geometry. Conversely, the algebraic geometry of toric varieties gives new insight into continued fractions as well as their higher-dimensional analogues, the isoperimetric problem and other questions on convex bodies. Relevant results on convex geometry are collected together in the appendix.
Author | : Paul A. Schweitzer |
Publisher | : American Mathematical Soc. |
Total Pages | : 306 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 0821851705 |
Download Differential Topology, Foliations, and Group Actions Book in PDF, ePub and Kindle
This volume contains the proceedings of the Workshop on Topology held at the Pontificia Universidade Catolica in Rio de Janeiro in January 1992. Bringing together about one hundred mathematicians from Brazil and around the world, the workshop covered a variety of topics in differential and algebraic topology, including group actions, foliations, low-dimensional topology, and connections to differential geometry. The main concentration was on foliation theory, but there was a lively exchange on other current topics in topology. The volume contains an excellent list of open problems in foliation research, prepared with the participation of some of the top world experts in this area. Also presented here are two surveys on group actions---finite group actions and rigidity theory for Anosov actions---as well as an elementary survey of Thurston's geometric topology in dimensions 2 and 3 that would be accessible to advanced undergraduates and graduate students.