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Author:   Maxim E. Kazaryan ,  Sergei K. Lando ,  Victor V. Prasolov ,  Natalia Tsilevich
Publisher:   Springer Nature Switzerland AG
Imprint:   Springer Nature Switzerland AG
Edition:   1st ed. 2018
Volume:   2
Weight:   0.541kg
ISBN:  

9783030029425

ISBN 10:   3030029425
Pages:   231
Publication Date:   06 February 2019
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Language:   English

Table of Contents

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.

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)

Author Information

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.

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