$I$-functions of Calabi--Yau 3-folds in Grassmannians

TL;DR

This paper investigates the $I$-functions associated with Calabi--Yau 3-folds embedded in Grassmannians, focusing on those with Picard number one, to understand their enumerative geometry.

Contribution

It introduces a systematic study of $I$-functions for Calabi--Yau 3-folds realized as zero loci of sections of homogeneous bundles on Grassmannians, expanding the understanding of their mirror symmetry.

Findings

Derived explicit formulas for $I$-functions of these Calabi--Yau 3-folds.

Established connections between $I$-functions and enumerative invariants.

Provided new computational tools for mirror symmetry in Grassmannian settings.

Abstract

We study $I$-functions of Calabi--Yau 3-folds with Picard number one which are zero loci of general sections of direct sums of globally generated irreducible homogeneous vector bundles on Grassmannians.