Higher order selfdual toric varieties

TL;DR

This paper characterizes higher order selfdual toric varieties using geometric and combinatorial methods, exploring their relations with Cayley-Bacharach questions and configurations, and providing examples and constructions.

Contribution

It offers new geometric and combinatorial characterizations of higher order selfdual toric varieties, expanding understanding of their structure and properties.

Findings

Characterization of higher order selfdual toric embeddings

Connections with Cayley-Bacharach questions

Examples and constructions of such varieties

Abstract

The notion of higher order dual varieties of a projective variety, introduced in \cite{P83}, is a natural generalization of the classical notion of projective duality. In this paper we present geometric and combinatorial characterizations of those equivariant projective toric embeddings that satisfy higher order selfduality. We also give several examples and general constructions. In particular, we highlight the relation with Cayley-Bacharach questions and with Cayley configurations.