Description
This first volume provides a thorough introduction to Hodge theory, one of the most important tools in modern algebraic geometry. Written by renowned mathematician Claire Voisin and translated by Leila Schneps, the book systematically develops the theory from its foundations.
The text covers essential topics including harmonic forms, Kähler geometry, and the Hodge decomposition theorem. It explores how cohomology groups of complex algebraic varieties can be equipped with rich additional structures, enabling deep insights into their geometric properties.
Designed for graduate students and researchers, this work balances rigor with accessibility. The careful exposition of abstract concepts is complemented by concrete examples and applications. The volume serves as an essential reference for understanding the interplay between differential geometry, algebraic topology, and algebraic geometry, making it indispensable for anyone studying modern geometry.
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