This is a brief textbook on complex analysis intended for the
students of upper undergraduate or beginning graduate level. The
author stresses the aspects of complex analysis that are most
important for the student planning to study algebraic geometry and
related topics. The exposition is rigorous but elementary: abstract
notions are introduced only if they are really indispensable. This
approach provides a motivation for the reader to digest more
abstract definitions (e.g., those of sheaves or line bundles, which
are not mentioned in the book) when he/she is ready for that level
of abstraction indeed. In the chapter on Riemann surfaces, several
key results on compact Riemann surfaces are stated and proved in
the first nontrivial case, i.e. that of elliptic curves.
General
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