Towards small quantum Chern character

TL;DR

This paper develops a quantum analogue of the classical Chern character homomorphism for specific algebraic varieties, linking quantum K-theory and quantum cohomology, and provides a ring presentation for Milnor hypersurfaces.

Contribution

It introduces a quantum Chern character homomorphism for projective spaces and incidence varieties, extending classical concepts into the quantum realm.

Findings

Quantum Chern character homomorphism constructed for projective spaces and incidence varieties.

Ring presentation of small quantum K-theory for Milnor hypersurfaces provided.

Classical limit recovers the classical Chern character homomorphism.

Abstract

We show a quantum version of Chern character homomorphism from the small quantum K-theory to the small quantum cohomology in the cases of projective spaces and incidence varieties, whose classical limit gives the classical Chern character homomorphism. We also provide a ring presentation of the small quantum K-theory of Milnor hypersurfaces.