“The book is an excellent contribution to the literature, offering valuable insights into Hadamard products of projective varieties. Its clear writing, well-organized content, computational tools, and discussion of open problems make it particularly useful for students and early-career researchers seeking to delve deeper into this topic.” (Le Ngoc Long, Mathematical Reviews, July, 2025)
“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.” (Wael Badawy, Computing Reviews, November 25, 2024)
This monograph deals with the Hadamard products of algebraic varieties. A typical subject of study in Algebraic Geometry are varieties constructed from other geometrical objects. The most well-known example is constituted by the secant varieties, which are obtained through the construction of the join of two algebraic varieties, which, in turn, is based on the operation of summing two vectors. However, other constructions are possible through a change of the basic operation. One remarkable case is based on the Hadamard product of two vectors. While secant varieties of algebraic varieties have been studied extensively and systematically, the same is not yet true for the Hadamard products of algebraic varieties. This monograph aims to bridge this gap in the literature.
The topic is presented in a self-contained manner, and it is accessible to all readers with sound knowledge of Commutative Algebra and Algebraic Geometry. Both experienced researchers and students can profit from this monograph, which will guide them through the subject. The foundational aspects of the Hadamard products of algebraic varieties are covered and some connections both within and outside Algebraic Geometry are presented. The theoretical and algorithmic aspects of the subject are considered to demonstrate the effectiveness of the results presented. Thus, this monograph will also be useful to researchers in other fields, such as Algebraic Statistics, since it provides several algebraic and geometric results on such products.
