Hadamard Products of Linear Spaces
Cristiano Bocci, Enrico Carlini, Joe Kileel
TL;DR
This paper explores the properties of Hadamard products of algebraic varieties, revealing that Hadamard powers of lines are linear spaces and using tropical geometry to determine degrees of products.
Contribution
It introduces new geometric properties of Hadamard products and employs tropical geometry to analyze degrees of these products for linear spaces.
Findings
Hadamard power of a line is a linear space
Star configurations can be constructed from collinear points
Tropical geometry helps find degrees of Hadamard products
Abstract
We describe properties of Hadamard products of algebraic varieties. We show any Hadamard power of a line is a linear space, and we construct star configurations from products of collinear points. Tropical geometry is used to find the degree of Hadamard products of other linear spaces.
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