Cristiano Bocci and Enrico Carlini offer a detailed and much-needed exploration of the Hadamard products of algebraic varieties--a relatively underexplored area in algebraic geometry. Their monograph bridges a significant gap in the literature by focusing on how algebraic varieties can be constructed through operations other than the traditional vector summation, specifically through the Hadamard product. The book serves as an excellent resource for researchers interested in commutative algebra, algebraic geometry, and related fields.

Hadamard products of projective varieties presents “foundational aspects of the Hadamard products of algebraic varieties,” ensuring that the subject is accessible to both seasoned researchers and advanced students. While secant varieties have been extensively studied, this book opens the door to studying Hadamard products, which offer a new perspective in the field. By combining theoretical insights with algorithmic approaches, the authors make the subject approachable for those working in algebraic statistics and combinatorial commutative algebra, fields where these geometric constructions have practical applications.

One of the book’s strengths is its self-contained nature. Even though the topic is advanced, the authors ensure that readers with a solid foundation in algebraic geometry and commutative algebra will find the book accessible and rewarding. However, beginners may find the topic challenging without prior knowledge of these subjects.

Similar books include Commutative algebra [1], a classic introduction connecting commutative algebra and algebraic geometry, and Ideals, varieties, and algorithms [2], a more accessible entry point for those new to algebraic geometry and computational methods.