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Moscow Lectures

Algebraic Curves

Towards Moduli Spaces

Authors: Kazaryan, Maxim E., Lando, Sergei K., Prasolov, Victor

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  • Leads a reader to far advanced topics widely used in modern research, using basic tools from the first two years of university studies
  • From the very beginning, the study of algebraic curves is aimed at the construction of their moduli spaces in the final chapters
  • Supplied with numerous exercises and problems both making the book a convenient base for a university lecture course and allowing the reader to control his/her progress
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eBook $59.99
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  • ISBN 978-3-030-02943-2
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  • Immediate eBook download after purchase
Hardcover $74.99
price for USA
  • ISBN 978-3-030-02942-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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

About the authors

Maxim Kazaryan is a researcher at the Steklov Mathematical Institute RAS. He also works as a professor of mathematics at the NRU Higher School of Economics since 2008 and at the Skolkovo Institute of Science and Technology since 2016.

Sergei Lando is a professor of mathematics at the NRU Higher School of Economics since 2008 and at the Skolkovo Institute of Science and Technology since 2016. He was the first Dean of the Department of Mathematics at the NRU HSE. He also is a Vice-President of the Moscow Mathematical Society.

Victor Prasolov is a permanent teacher of mathematics at the Independent University of Moscow.

Reviews

“The book under review is an accessible introduction to the study of complex algebraic curves and their moduli spaces. … The book comes with sets of exercises in each of its chapters and can be used as a textbook for a graduate course or for self-study by a motivated reader.” (Felipe Zaldivar, MAA Reviews, April 22, 2019)


Table of contents (19 chapters)

Table of contents (19 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-030-02943-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.99
price for USA
  • ISBN 978-3-030-02942-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.

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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Curves
Book Subtitle
Towards Moduli Spaces
Authors
Translated by
Tsilevich, N.
Series Title
Moscow Lectures
Series Volume
2
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-02943-2
DOI
10.1007/978-3-030-02943-2
Hardcover ISBN
978-3-030-02942-5
Series ISSN
2522-0314
Edition Number
1
Number of Pages
XIV, 231
Number of Illustrations
37 b/w illustrations
Topics