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＜電子ブック＞
Hadamard Products of Projective Varieties / by Cristiano Bocci, Enrico Carlini
(Frontiers in Mathematics. ISSN:16608054)

版	1st ed. 2024.
出版者	(Cham : Springer Nature Switzerland : Imprint: Birkhäuser)
出版年	2024
本文言語	英語
大きさ	XIX, 243 p. 9 illus : online resource
著者標目	*Bocci, Cristiano author Carlini, Enrico author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Projective geometry LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Commutative algebra LCSH:Commutative rings FREE:Algebraic Geometry FREE:Projective Geometry FREE:Symbolic and Algebraic Manipulation FREE:Commutative Rings and Algebras
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-031-54263-3

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