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

Brian Forbes (Research Institute for Mathematical Sciences, Kyoto University, Japan)

Masao Jinzenji (Division of Mathematics, Graduate School of Science, Hokkaido University, Sapporo, Japan)

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 $\oo(k)\oplus \oo(-2-k)\rightarrow \p^1$.

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