Discriminants and toric K-theory

TL;DR

This paper explores a categorical framework for discriminants using combinatorial language, inspired by homological mirror symmetry, and provides K-theoretic evidence supporting a conjecture related to this theory.

Contribution

It introduces a novel categorical approach to discriminants in the context of homological mirror symmetry, offering new K-theoretic insights and evidence for a conjecture.

Findings

Provides K-theoretic evidence for Aspinwall's conjecture

Develops a categorical approach to discriminants

Connects homological mirror symmetry with discriminant theory

Abstract

We discuss a categorical approach to the theory of discriminants in the combinatorial language introduced by Gelfand, Kapranov and Zelevinsky. Our point of view is inspired by homological mirror symmetry and provides $K$--theoretic evidence for a conjecture presented by Paul Aspinwall in a conference talk in Banff in March 2016 and later in a joint paper with Plesser and Wang.