T-structures on a local 4-Calabi-Yau variety

TL;DR

This paper investigates t-structures in the derived category of a non-compact Calabi-Yau 4-fold, specifically the cotangent bundle of the projective plane, using tilting objects to classify and analyze their combinatorial properties.

Contribution

It introduces a method to characterize and compute a broad class of t-structures on a local Calabi-Yau 4-fold via tilting objects.

Findings

Classification of t-structures using tilting objects

Calculation of combinatorics of t-structures

Characterization of large classes of t-structures

Abstract

Let $X$ denote the total space of cotangent bundle of projective plane. This is a non-compact Calabi-Yau $4$-fold (also called local Calabi-Yau variety in physics literature). The aim of this paper is to use tilting objects to characterize a large class of t-structures in the relevant Calabi-Yau category and try to calculate the combinatorics of them.