On equivariant mirror symmetry for local P^2

TL;DR

This paper advances the understanding of equivariant mirror symmetry for local P^2 by decomposing it into simpler subproblems and offers a new perspective on mirror symmetry for certain line bundle sums over P^1.

Contribution

It provides a solution to equivariant mirror symmetry for O(-3) over P^2 with one equivariant parameter, decomposing the problem into three independent subspaces.

Findings

Decomposition of mirror symmetry for local P^2 into three subspaces.

Solution of equivariant mirror symmetry for O(-3) over P^2.

New interpretation of mirror symmetry for O(k)+O(-2-k) over P^1.

Abstract

We solve the problem of equivariant mirror symmetry for O(-3)->P^2 for the (three) cases of one independent equivariant parameter. This gives a decomposition of mirror symmetry for local P^2 into that of three subspaces, each of which may be considered independently. Finally, we give a new interpretation of mirror symmetry for O(k)+O(-2-k)->P^1.