國立高雄大學圖資館 |

Language: English

Back

Hadamard products of projective varieties

Record Type:	Electronic resources : Monograph/item
Title/Author:	Hadamard products of projective varietiesby Cristiano Bocci, Enrico Carlini.
Author:	Bocci, Cristiano.
other author:	Carlini, Enrico.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xix, 243 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Geometry, Algebraic.
Online resource:	https://doi.org/10.1007/978-3-031-54263-3
ISBN:	9783031542633$q(electronic bk.)

Hadamard products of projective varieties
Bocci, Cristiano.

Hadamard products of projective varieties[electronic resource] /by Cristiano Bocci, Enrico Carlini. - Cham :Springer Nature Switzerland :2024. - xix, 243 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8054. - Frontiers in mathematics..

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.

ISBN: 9783031542633$q(electronic bk.)

Standard No.: 10.1007/978-3-031-54263-3doiSubjects--Topical Terms:

190843
Geometry, Algebraic.

LC Class. No.: QA564

Dewey Class. No.: 516.35

Hadamard products of projective varieties
LDR:02820nmm a22003375a 4500 001 665334
003 DE-He213
005 20240327004316.0
006 m d
007 cr nn 008maaau
008 241219s2024 sz s 0 eng d
020 $a 9783031542633$q(electronic bk.)
020 $a 9783031542626$q(paper)
024 7 $a 10.1007/978-3-031-54263-3 $2 doi
035 $a 978-3-031-54263-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA564
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 516.35 $2 23
090 $a QA564 $b .B664 2024
100 1 $a Bocci, Cristiano. $3 852188
245 1 0 $a Hadamard products of projective varieties $h [electronic resource] / $c by Cristiano Bocci, Enrico Carlini.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Birkhäuser, $c 2024.
300 $a xix, 243 p. : $b ill., digital ; $c 24 cm.
490 1 $a Frontiers in mathematics, $x 1660-8054
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.
650 0 $a Geometry, Algebraic. $3 190843
650 0 $a Hadamard matrices. $3 184604
650 1 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Projective Geometry. $3 676333
650 2 4 $a Symbolic and Algebraic Manipulation. $3 273720
650 2 4 $a Commutative Rings and Algebras. $3 274057
700 1 $a Carlini, Enrico. $3 869337
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Frontiers in mathematics. $3 558254
856 4 0 $u https://doi.org/10.1007/978-3-031-54263-3
950 $a Mathematics and Statistics (SpringerNature-11649)