Hadamard products of hypersurfaces

TL;DR

This paper characterizes hypersurfaces whose Hadamard product remains a hypersurface and explores varieties that are idempotent under Hadamard powers, advancing understanding of algebraic structures under Hadamard operations.

Contribution

It provides the first characterization of hypersurfaces preserved under Hadamard products and studies idempotent varieties under Hadamard powers, revealing new algebraic properties.

Findings

Identified conditions for hypersurfaces to remain hypersurfaces after Hadamard product

Characterized idempotent hypersurfaces under Hadamard powers

Extended analysis to general varieties with Hadamard power idempotency

Abstract

In this paper we, first, characterize hypersurfaces for which their Hadamard product is still a hypersurface. Then we pass to study hypersurfaces and, more generally, varieties which are idempotent under Hadamard powers.