The Candelas-de la Ossa-Green-Parkes formula

Bong H Lian Kefeng Liu Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43108

Nuclear Physics B-Proceedings Supplements, 67, 106-114, 1998.7
In this note we discuss a recent proof of the formula for the worldsheet instanton prepotential predicted by Mirror Symmetry for the quintics in <b>P</b><sup>4</sup>. One of the key ingredients in the proof is the equivariant cohomology groups on the so-called linear sigma model moduli spaces. We introduce the notion of admissible data on the equivariant cohomology groups of the linear sigma model. An admissible data may be thought of as a sequence of equivariant classes satisfying certain algebraic conditions. It arises naturally from Kontsevich's stable map compactification of moduli spaces of maps from curves into projective manifolds. The structures of admissible data help reduce many counting problems to checking certain combinatorial structure of a compactification. The mirror transformation of Candelas et al turns out to be a transformation between two admissible data associated respectively to the linear and the non-linear
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  title={The Candelas-de la Ossa-Green-Parkes formula},
  author={Bong H Lian, Kefeng Liu, and Shing-Tung Yau},
  booktitle={Nuclear Physics B-Proceedings Supplements},
Bong H Lian, Kefeng Liu, and Shing-Tung Yau. The Candelas-de la Ossa-Green-Parkes formula. 1998. Vol. 67. In Nuclear Physics B-Proceedings Supplements. pp.106-114.
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