03927nam a22005775i 4500 978-3-031-54263-3 DE-He213 20251030111746.0 cr nn 008mamaa 240327s2024 sz | s |||| 0|eng d 9783031542633 978-3-031-54263-3 10.1007/978-3-031-54263-3 doi QA564-609 PBMW bicssc MAT012010 bisacsh PBMW thema Bocci, Cristiano. author. aut http://id.loc.gov/vocabulary/relators/aut 74055 Hadamard Products of Projective Varieties [electronic resource] / by Cristiano Bocci, Enrico Carlini. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024. XIX, 243 p. 9 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontiers in Mathematics, 1660-8054 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. 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. Algebraic geometry. Projective geometry. 74056 Computer science Mathematics. 64041 Commutative algebra. 70151 Commutative rings. 70152 Algebraic Geometry. Projective Geometry. 74057 Symbolic and Algebraic Manipulation. Commutative Rings and Algebras. 70156 Carlini, Enrico. author. aut http://id.loc.gov/vocabulary/relators/aut 74058 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031542626 Printed edition: 9783031542640 Frontiers in Mathematics, 1660-8054 72228 https://doi.org/10.1007/978-3-031-54263-3 ZDB-2-SMA ZDB-2-SXMS 58681 58681