Hadamard Products of Projective Varieties
Bocci, Cristiano, Carlini, Enrico
- 出版商: Birkhauser Boston
- 出版日期: 2024-03-28
- 售價: $2,540
- 貴賓價: 9.5 折 $2,413
- 語言: 英文
- 頁數: 243
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031542622
- ISBN-13: 9783031542626
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商品描述
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.
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.
商品描述(中文翻譯)
本專著探討代數簇的Hadamard乘積。代數幾何中的一個典型研究主題是由其他幾何物件構造的簇。最著名的例子是割線簇,這是通過構造兩個代數簇的連接而獲得的,而這一過程又基於兩個向量的相加運算。然而,通過改變基本運算,還可以進行其他構造。一個顯著的案例是基於兩個向量的Hadamard乘積。儘管代數簇的割線簇已被廣泛且系統地研究,但代數簇的Hadamard乘積尚未得到同樣的重視。本專著旨在填補文獻中的這一空白。
該主題以自足的方式呈現,對於具備良好交換代數和代數幾何知識的讀者來說是可接觸的。無論是經驗豐富的研究人員還是學生,都能從本專著中獲益,該專著將引導他們深入了解該主題。專著涵蓋了代數簇的Hadamard乘積的基礎方面,並呈現了一些在代數幾何內部及外部的聯繫。該主題的理論和演算法方面也被考慮,以展示所呈現結果的有效性。因此,本專著對於其他領域的研究人員也將是有用的,例如代數統計,因為它提供了有關這些乘積的多個代數和幾何結果。
作者簡介
Cristiano Bocci is a full Professor in geometry at the Department of Information Engineering and Mathematics of the Università di Siena, Italy. His research interests focus on Algebraic Geometry, Combinatorial Commutative Algebra, Algebraic Statistics and Biomathematics. Enrico Carlini is a full Professor in geometry at the Department of Mathematical Sciences of the Politecnico di Torino, in Turin, Italy. His research interests focus on the interactions between Algebraic Geometry and Commutative Algebra and on their applications.
作者簡介(中文翻譯)
Cristiano Bocci 是義大利錫耶納大學資訊工程與數學系的全職幾何教授。他的研究興趣集中在代數幾何、組合交換代數、代數統計和生物數學。
Enrico Carlini 是義大利都靈理工大學數學科學系的全職幾何教授。他的研究興趣集中在代數幾何與交換代數之間的相互作用及其應用。