عنوان

Algebraic curves :

(Number (ISBN

3030029425

(Number (ISBN

3030029433

(Number (ISBN

3030029441

(Number (ISBN

9783030029425

(Number (ISBN

9783030029432

(Number (ISBN

9783030029449

Erroneous ISBN

9783030029425

Title Proper

Algebraic curves :

General Material Designation

[Book]

Other Title Information

towards Moduli spaces /

First Statement of Responsibility

Maxim E. Kazaryan, Sergei K. Lando, Victor V. Prasolov.

Place of Publication, Distribution, etc.

Cham, Switzerland :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

2018.

Specific Material Designation and Extent of Item

1 online resource (xiv, 231 pages) :

Other Physical Details

illustrations

Series Title

Moscow Lectures,

Volume Designation

volume 2

ISSN of Series

2522-0314 ;

Text of Note

Includes bibliographical references and index.

Text of Note

Introduction.- 1 Preliminaries -- 2 Algebraic curves.- 3 Complex structure and the topology of curves.- 4 Curves in projective spaces.- 5 Plücker formulas.- 6 Mappings of curves.- 7 Differential 1-forms on curves.- 8 Line bundles, linear systems, and divisors.- 9 Riemann-Roch formula and its applications.- 10 Proof of the Riemann-Roch formula.- 11 Weierstrass points.- 12 Abel's theorem.- 13 Examples of moduli spaces.- 14 Approaches to constructing moduli spaces.- 15 Moduli spaces of rational curves with marked points.- 16 Stable curves.- 17 A backward look from the viewpoint of characteristic classes.- 18 Moduli spaces of stable maps.- 19 Exam problems.- References.- Index.

0

Text of Note

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.

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9783030029432

International Standard Book Number

9783030029425

International Standard Book Number

9783030029449

Curves, Algebraic.

Moduli theory.

Curves, Algebraic.

Moduli theory.

MAT012010

PBMW

PBMW

Number

Edition

Class number

Kazaryan, Maxim E.

Lando, S. K., (Sergei K.),1955-

Prasolov, V. V., (Viktor Vasilʹevich)

Date of Transaction

20200823074804.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y