Hadamard Products of Projective Varieties

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 jo...

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Main Authors: Bocci, Cristiano (Author), Carlini, Enrico (Author)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:inglés
Publicado: Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024.
Edición:1st ed. 2024.
Series:Frontiers in Mathematics,
Subjects:
Acceso en liña:https://doi.org/10.1007/978-3-031-54263-3
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245 1 0 |a Hadamard Products of Projective Varieties  |h [electronic resource] /  |c by Cristiano Bocci, Enrico Carlini. 
250 |a 1st ed. 2024. 
264 1 |a Cham :  |b Springer Nature Switzerland :  |b Imprint: Birkhäuser,  |c 2024. 
300 |a XIX, 243 p. 9 illus.  |b online resource. 
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505 0 |a 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. 
520 |a 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. 
532 8 |a Accessibility summary: This PDF does not fully comply with PDF/UA standards, but does feature limited screen reader support, described non-text content (images, graphs), bookmarks for easy navigation and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. 
532 8 |a No reading system accessibility options actively disabled 
532 8 |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com 
650 0 |a Algebraic geometry. 
650 0 |a Projective geometry. 
650 0 |a Computer science  |x Mathematics. 
650 0 |a Commutative algebra. 
650 0 |a Commutative rings. 
650 1 4 |a Algebraic Geometry. 
650 2 4 |a Projective Geometry. 
650 2 4 |a Symbolic and Algebraic Manipulation. 
650 2 4 |a Commutative Rings and Algebras. 
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