Algebraic Curves, the Brill and Noether Way - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Curves, the Brill and Noether Way write by Eduardo Casas-Alvero. This book was released on 2019-11-30. Algebraic Curves, the Brill and Noether Way available in PDF, EPUB and Kindle. The book presents the central facts of the local, projective and intrinsic theories of complex algebraic plane curves, with complete proofs and starting from low-level prerequisites. It includes Puiseux series, branches, intersection multiplicity, Bézout theorem, rational functions, Riemann-Roch theorem and rational maps. It is aimed at graduate and advanced undergraduate students, and also at anyone interested in algebraic curves or in an introduction to algebraic geometry via curves.
The Brill-Noether Theorem for Real Algebraic Curves
The Brill-Noether Theorem for Real Algebraic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Brill-Noether Theorem for Real Algebraic Curves write by Sharad Chaudhary. This book was released on 1996. The Brill-Noether Theorem for Real Algebraic Curves available in PDF, EPUB and Kindle.
A Treatise on Algebraic Plane Curves
A Treatise on Algebraic Plane Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Treatise on Algebraic Plane Curves write by Julian Lowell Coolidge. This book was released on 2004-01-01. A Treatise on Algebraic Plane Curves available in PDF, EPUB and Kindle. A thorough introduction to the theory of algebraic plane curves and their relations to various fields of geometry and analysis. Almost entirely confined to the properties of the general curve, and chiefly employs algebraic procedure. Geometric methods are much employed, however, especially those involving the projective geometry of hyperspace. 1931 edition. 17 illustrations.
Brill--Noether Theory Over the Hurwitz Space
Brill--Noether Theory Over the Hurwitz Space - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Brill--Noether Theory Over the Hurwitz Space write by Hannah Kerner Larson. This book was released on 2022. Brill--Noether Theory Over the Hurwitz Space available in PDF, EPUB and Kindle. Historically, algebraic curves were defined as the solutions to a collection of polynomial equations inside of some ambient space. In the 19th century, however, mathematicians defined the notion of an abstract curve. With this perspective, the same abstract curve may sit in an ambient (projective) space in more than one way. The foundational Brill--Noether theorem, proved in the 1970s and 1980s, bridges these two perspectives by describing the maps of "most" abstract curves to projective spaces. However, the theorem does not hold for all curves. In nature, we often encounter curves already in (or mapping to) a projective space, and the presence of such a map may force the curve to have unexpected maps to other projective spaces! The first case of this is a curve that already has a map to the projective line. From the 1990s through the late 2010s, several mathematicians investigated this first case. They found that the space of maps of such a curve to other projective spaces can have multiple components of varying dimensions and eventually determined the dimension of the largest component. In this thesis, I develop analogues of all the main theorems of Brill--Noether theory for curves that already have a map to the projective line. The moduli space of curves together with a map to the line is called the Hurwitz space, so we call this work Brill--Noether theory over the Hurwitz space.
Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59
Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59 write by David Mumford. This book was released on 2016-03-02. Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59 available in PDF, EPUB and Kindle. These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.
