Hadamard Products of Projective Varieties

2024
ISBN: 978-3-031-54262-6
Verlag: Springer Nature Switzerland

Buch, Englisch, 243 Seiten, Format (B × H): 168 mm x 240 mm, Gewicht: 449 g

Reihe: Frontiers in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Carlini, Enrico

Bocci, Cristiano

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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.

Über Autor(innen)

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.