![]() | This article may be too technical for most readers to understand.(July 2020) |
In mathematics, mirror symmetry is a conjectural relationship between certain Calabi–Yau manifolds and a constructed "mirror manifold". The conjecture allows one to relate the number of rational curves on a Calabi-Yau manifold (encoded as Gromov–Witten invariants) to integrals from a family of varieties (encoded as period integrals on a variation of Hodge structures). In short, this means there is a relation between the number of genus algebraic curves of degree on a Calabi-Yau variety and integrals on a dual variety . These relations were original discovered by Candelas, de la Ossa, Green, and Parkes[1] in a paper studying a generic quintic threefold in as the variety and a construction[2] from the quintic Dwork family giving . Shortly after, Sheldon Katz wrote a summary paper[3] outlining part of their construction and conjectures what the rigorous mathematical interpretation could be.