Complex Manifolds and Geometric Algebraic Analysis

Complex Manifolds and Geometric Algebraic Analysis, 1st Edition, is a graduate textbook written by Ahmed Lesfari that provides a rigorous introduction to complex manifold theory and geometric algebraic analysis. Designed for graduate students in mathematics, physics, and related disciplines, the text establishes core analytical tools required for advanced geometric study.

The volume opens with the essential properties of holomorphic functions in several complex variables, quickly transitioning to methods for analyzing complex manifolds and analytic varieties. Subsequent chapters develop foundational machinery from sheaves and cohomology, which leads into detailed examinations of divisors, line bundles, and fundamental theorems within complex manifold theory.

Later chapters address the definitions and structural properties of abelian varieties, followed by an exploration of theta functions on complex projective tori. To reinforce comprehension across its ten chapters, the textbook includes worked examples, practice exercises, and a selection of problems accompanied by full solutions.