TY  - BOOK
AU  - Bocci,Cristiano
AU  - Carlini,Enrico
ED  - SpringerLink (Online service)
TI  - Hadamard Products of Projective Varieties
T2  - Frontiers in Mathematics,
SN  - 9783031542633
AV  - QA564-609 
PY  - 2024///
CY  - Cham
PB  - Springer Nature Switzerland, Imprint: Birkhäuser
KW  - Algebraic geometry
KW  - Projective geometry
KW  - Computer science
KW  - Mathematics
KW  - Commutative algebra
KW  - Commutative rings
KW  - Algebraic Geometry
KW  - Projective Geometry
KW  - Symbolic and Algebraic Manipulation
KW  - Commutative Rings and Algebras
N1  - Hadamard products -- Linear spaces -- Not generic cases in P2 -- Grids and rulings -- Degenerate varieties -- Hypersurfaces -- Binomial varieties -- Hilbert functions -- Star configurations -- Gorenstein sets of points in P3 -- Pure Commutative Algebra -- Open questions
N2  - 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
UR  - https://doi.org/10.1007/978-3-031-54263-3
ER  -