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# Communications in Number Theory and Physics

## Volume 1 (2007)

### Number 4

### On equivariant mirror symmetry for local $\p^2$

Pages: 729 – 760

DOI: http://dx.doi.org/10.4310/CNTP.2007.v1.n4.a5

#### Authors

#### Abstract

We solve the problem of equivariant mirror symmetry for$K_{\p^2}=\oo(-3)\rightarrow \p^2$ for the (three) cases of one independentequivariant parameter. This gives a decomposition of mirror symmetry for$K_{\p^2}$ into that of three subspaces, each of which may be consideredindependently. Finally, we give a new interpretation ofmirror symmetry for $\oo(k)\oplus \oo(-2-k)\rightarrow \p^1$.