Riemann surfaces (Q2865662)

This book is an introductory course on Riemann surfaces. The book is written in form of lecture notes and based on a cycle of lectures given by the author at the Steklov Institute in 2005.NEWLINENEWLINEThe eleven lectures of the course are combined into 5 chapters (topics). The book starts with an introduction to the theory of algebraic curves starting with the notion of algebraic functions, local parametrization and singular points, finishing with the Riemann-Hurwitz formula. The second chapter deals with topology of surfaces and differential forms on them. The complex structures of a surface are introduced in the next chpater.NEWLINENEWLINEThe central chapter, where the main approach is discussed in details, is called ``Around the operator \(\overline{\partial}\)''. Finally, divisors and an introduction to the theory of bundles are studied.NEWLINENEWLINEThe book is clearly written, supplied by a series of exercises. Surely it can be recommended as an introductory course on the subject.