Quantum Pieri rules for tautological subbundles

TL;DR

This paper establishes quantum Pieri rules for the quantum cohomology of classical type Grassmannians, linking Gromov-Witten invariants with classical intersection theory to facilitate computations of quantum products.

Contribution

It introduces explicit quantum Pieri rules for tautological subbundles in classical Grassmannians, connecting Gromov-Witten invariants with classical intersection numbers.

Findings

Quantum Pieri rules derived for classical Grassmannians.

Gromov-Witten invariants coincide with classical intersection numbers.

Facilitates computation of quantum products in cohomology.

Abstract

We give quantum Pieri rules for quantum cohomology of Grassmannians of classical types, expressing the quantum product of Chern classes of the tautological subbundles with general cohomology classes. We derive them by showing the relevant genus zero, three-pointed Gromov-Witten invariants coincide with certain classical intersection numbers.