Algebraic curves. Towards moduli spaces. Translated from the Russian by Natalia Tsilevich
type: Item
instance of: scholarly article
title: Algebraic curves. Towards moduli spaces. Translated from the Russian by Natalia Tsilevich
zbMATH Open document ID: 1410.14025
DOI: 10.1007/978-3-030-02943-2
author: M. È. Kazaryan
author: S. Lando
author: V. V. Prasolov
published in: Moscow Lectures
publication date: 2018-11-21T00:00:00Z
review text: This book focuses on the theory of Riemann surfaces from the modern viewpoint of complex algebraic curves and their moduli spaces. Chapters 1--3 introduce preliminaries of curves, including their algebraic structure, complex structure, topology, branched coverings, realization in the plane, and rational parametrization. Chapters 4--6 study curves in projective spaces, Plücker Formulas, and mappings of curves with a focus on elliptic curves. Chapters 7--12 highlight classical objects associated with curves, including differential forms, line bundles and divisors, Riemann-Roch Formula, Weierstrass points, and Jacobian. Chapters 13--18 focus on various moduli spaces, including Hilbert schemes, moduli spaces of curves with marked points, and moduli spaces of stable maps. Finally in Chapter 19 many exam questions are given to test the reader's understanding of the subject.
reviewed by: Dawei Chen
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14H50
zbMATH DE Number: 6982465
zbMATH Keywords: algebraic curve
zbMATH Keywords: Riemann surface
zbMATH Keywords: moduli space
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-030-02943-2
OpenAlex ID: W4231116035
Recommended article: Q4327355
Recommended article: Q4385503
Recommended article: Q4830321
Recommended article: Algebraic geometry I: algebraic curves, algebraic manifolds and schemes. Transl. from the Russian by D. Coray and V. N. Shokurov
Recommended article: Algebraic geometry. Transl. from the Russian
Recommended article: Q4418886
Recommended article: Q4528913
Recommended article: Q3825180
Recommended article: Q5484940
Recommended article: Tautological algebras of moduli spaces of curves
description: scientific article; zbMATH DE number 6982465