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The Chen-Ruan Cohomology Ring of Mirror Quintic

B. Doug Park·Mainak Poddar
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Abstract

We compute the Chen-Ruan orbifold cohomology ring of the Batyrev mirror orbifold of a smooth quintic hypersurface in 4-dimensional projective space. We identify the obstruction bundle for this example by using the Riemann bilinear relations for periods. We outline a general method of computing the Chen-Ruan ring for Calabi-Yau hypersurfaces in projective simplicial toric varieties, modulo a conjecture that the Riemann bilinear relations are adequate for identifying the obstruction bundle for any complex orbifold.

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B. Doug Park, Mainak Poddar. 2002-10-12. The Chen-Ruan Cohomology Ring of Mirror Quintic. https://arxiv.org/abs/math/0210185

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