Author: Linnaeus Wayland DowlingPublisher:
ISBN:
Category : Curves, Quintic
Languages : en
Pages : 36
Book Description
On the Forms of Plane Quintic Curves
Author: Linnaeus Wayland DowlingPublisher:
ISBN:
Category : Curves, Quintic
Languages : en
Pages : 36
Book Description
Plane Quartic Curves Obtained by Quadratic Transformation of Curves of Lower Order
Author: Leon BattigClassical Algebraic Geometry
Author: Igor V. DolgachevPublisher: Cambridge University Press
ISBN: 1139560786
Category : Mathematics
Languages : en
Pages : 653
Book Description
Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.
A Catalog of Special Plane Curves
Author: J. Dennis LawrencePublisher: Courier Corporation
ISBN: 0486167666
Category : Mathematics
Languages : en
Pages : 244
Book Description
DIVOne of the most beautiful aspects of geometry. Information on general properties, derived curves, geometric and analytic properties of each curve. 89 illus. /div
Singularities of Plane Curves
Author: Eduardo Casas-AlveroPublisher: Cambridge University Press
ISBN: 0521789591
Category : Mathematics
Languages : en
Pages : 363
Book Description
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.
Algebraic Curves
Author: William FultonPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 120
Book Description
The aim of these notes is to develop the theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. We have assumed that the reader is familiar with some basic properties of rings, ideals and polynomials, such as is often covered in a one-semester course in modern algebra; additional commutative algebra is developed in later sections.
An Invitation to Quantum Cohomology
Author: Joachim KockPublisher: Springer Science & Business Media
ISBN: 0817644954
Category : Mathematics
Languages : en
Pages : 162
Book Description
Elementary introduction to stable maps and quantum cohomology presents the problem of counting rational plane curves Viewpoint is mostly that of enumerative geometry Emphasis is on examples, heuristic discussions, and simple applications to best convey the intuition behind the subject Ideal for self-study, for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory
An Introduction to the Theory of Multiply Periodic Functions
Author: Henry Frederick BakerPublisher:
ISBN:
Category : Functions
Languages : en
Pages : 360
Book Description
Geometry of Algebraic Curves
Author: Enrico ArbarelloPublisher: Springer
ISBN: 9781475753240
Category : Mathematics
Languages : en
Pages : 387
Book Description
In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 1950's and 1960's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory. It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre sents a significant advance beyond the legacy left by the classical geometers such as Noether, Castelnuovo, Enriques, and Severi. These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Along the way we shall, of course, discuss appli cations of the theory of linear series to a number of classical topics (e.g., the geometry of the Riemann theta divisor) as well as to some of the current research (e.g., the Kodaira dimension of the moduli space of curves).
Algebraic Geometry and Theta Functions
Author: Arthur B. CoblePublisher: American Mathematical Soc.
ISBN: 0821846027
Category : Mathematics
Languages : en
Pages : 292
Book Description
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and genus three (Chapter IV). The case of genus four is discussed in the last chapter. The exposition is concise with a rich variety of details and references.