The Analysis and Construction of Some Cubic Curves
Author : Sidney Teweles
Publisher :
Page : 114 pages
File Size : 17,80 MB
Release : 1937
Category : Curves, Cubic
ISBN :
Author : Sidney Teweles
Publisher :
Page : 114 pages
File Size : 17,80 MB
Release : 1937
Category : Curves, Cubic
ISBN :
Author : Maxim E. Kazaryan
Publisher : Springer
Page : 231 pages
File Size : 16,70 MB
Release : 2019-01-21
Category : Mathematics
ISBN : 3030029433
This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework
Author :
Publisher :
Page : pages
File Size : 40,56 MB
Release : 2001
Category :
ISBN :
An n-ary Steiner law f(x[sub 1], x[sub 2], [hor-ellipsis], x[sub n]) on a projective curve[Gamma] over an algebraically closed field k is a totally symmetric n-ary morphism f from[Gamma][sup n] to[Gamma] satisfying the universal identity f(x[sub 1], x[sub 2], [hor-ellipsis], x[sub n-1], f(x[sub 1], x[sub 2], [hor-ellipsis], x[sub n]))= x[sub n]. An element e in[Gamma] is called an idempotent for f if f(e, e, [hor-ellipsis], e)= e. The binary morphism x* y of the classical chord-tangent construction on a nonsingular cubic curve is an example of a binary Steiner law on the curve, and the idempotents of* are precisely the inflection points of the curve. In this paper, the authors prove that if f and g are two 5-ary Steiner laws on an elliptic curve[Gamma] sharing a common idempotent, then f= g. They use a new rule of inference rule=(gL)[implies], extracted from a powerful local-to-global principal in algebraic geometry. This rule is implemented in the theorem-proving program OTTER. Then they use OTTER to automatically prove the uniqueness of the 5-ary Steiner law on an elliptic curve. Very much like the binary case, this theorem provides an algebraic characterization of a geometric construction process involving conics and cubics. The well-known theorem of the uniqueness of the group law on such a curve is shown to be a consequence of this result.
Author : Alfred Barnard Basset
Publisher :
Page : 284 pages
File Size : 47,64 MB
Release : 1901
Category : Curves, Cubic
ISBN :
Author : A. B. Basset
Publisher : Forgotten Books
Page : 276 pages
File Size : 11,95 MB
Release : 2015-06-25
Category : Mathematics
ISBN : 9781330871584
Excerpt from An Elementary Treatise on Cubic and Quartic Curves The present work originated in certain notes, made about twenty-five years ago, upon the properties of some of the best-known higher plane curves; but upon attempting to revise them for the press, it appeared to me impossible to discuss the subject adequately without investigating the theory of the singularities of algebraic curves. I have accordingly included Plucker's equations, which determine the number and the species of the simple singularities of any algebraic curve; and have also considered all the compound singularities which a quartic curve can possess. This treatise is intended to be an elementary one on the subject. I have therefore avoided investigations which would require a knowledge of Modern Algebra, such as the theory of the invariants, covariants and other concomitants of a ternary quantic; and have assumed scarcely any further knowledge of analysis on the part of the reader, than is to be found in most of the ordinary text-books on the Differential Calculus and on Analytical Geometry. I have also endeavoured to give special prominence to geometrical methods, since the experience of many years has convinced me that a judicious combination of geometry and analysis is frequently capable of shortening and simplifying, what would otherwise be a tedious and lengthy investigation. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author : Debabrata Ray
Publisher : John Wiley & Sons
Page : 996 pages
File Size : 14,42 MB
Release : 2015-12-14
Category : Technology & Engineering
ISBN : 111899695X
Comprehensively introduces linear and nonlinear structural analysis through mesh generation, solid mechanics and a new numerical methodology called c-type finite element method Takes a self-contained approach of including all the essential background materials such as differential geometry, mesh generation, tensor analysis with particular elaboration on rotation tensor, finite element methodology and numerical analysis for a thorough understanding of the topics Presents for the first time in closed form the geometric stiffness, the mass, the gyroscopic damping and the centrifugal stiffness matrices for beams, plates and shells Includes numerous examples and exercises Presents solutions for locking problems
Author : Nickolas S. Sapidis
Publisher : SIAM
Page : 316 pages
File Size : 24,49 MB
Release : 1994-01-01
Category : Computers
ISBN : 0898713323
The authors define fairness mathematically, demonstrate how newly developed curve and surface schemes guarantee fairness, and assist the user in identifying and removing shape aberrations in a surface model without destroying the principal shape characteristics of the model. A valuable resource for engineers working in CAD, CAM, or computer-aided engineering.
Author :
Publisher :
Page : 776 pages
File Size : 43,31 MB
Release : 1971
Category : Mechanics, Applied
ISBN :
Author : M. Henrard
Publisher : Springer
Page : 300 pages
File Size : 11,98 MB
Release : 2014-05-29
Category : Business & Economics
ISBN : 1137374667
Following the financial crisis dramatic market changes, a new standard in interest rate modelling emerged, called the multi-curve framework. The author provides a detailed analysis of the framework, through its foundations, evolution and implementation. The book also covers recent extensions to collateral and stochastic spreads modelling.
Author : University of Hawaii (Honolulu). Land Study Bureau
Publisher :
Page : 160 pages
File Size : 28,6 MB
Release : 1964
Category : Agriculture
ISBN :