عنوان

Algebraic curves :

شابک

3030029425

شابک

3030029433

شابک

3030029441

شابک

9783030029425

شابک

9783030029432

شابک

9783030029449

شابک اشتباه

9783030029425

عنوان اصلي

Algebraic curves :

نام عام مواد

[Book]

ساير اطلاعات عنواني

towards Moduli spaces /

نام نخستين پديدآور

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

محل نشرو پخش و غیره

Cham, Switzerland :

نام ناشر، پخش کننده و غيره

Springer,

تاریخ نشرو بخش و غیره

2018.

نام خاص و کميت اثر

1 online resource (xiv, 231 pages) :

ساير جزييات

illustrations

عنوان فروست

Moscow Lectures,

مشخصه جلد

volume 2

شاپا ي ISSN فروست

2522-0314 ;

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

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.

بدون عنوان

0

متن يادداشت

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.

منبع سفارش / آدرس اشتراک

Springer Nature

شماره انبار

com.springer.onix.9783030029432

شماره استاندارد بين المللي کتاب و موسيقي

9783030029425

شماره استاندارد بين المللي کتاب و موسيقي

9783030029449

موضوع مستند نشده

Curves, Algebraic.

موضوع مستند نشده

Moduli theory.

موضوع مستند نشده

Curves, Algebraic.

موضوع مستند نشده

Moduli theory.

موضوع مستند نشده

MAT012010

موضوع مستند نشده

PBMW

موضوع مستند نشده

PBMW

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Kazaryan, Maxim E.

مستند نام اشخاص تاييد نشده

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

مستند نام اشخاص تاييد نشده

Prasolov, V. V., (Viktor Vasilʹevich)

تاريخ عمليات

20200823074804.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y