Transposition mirror symmetry construction and period integrals

Details Transposition mirror symmetry construction and period integrals Transposition mirror symmetry construction and period integrals

2005-06-17

arxiv.org/abs/math/0506354v3

Mathematics

Algebraic Geometry

20pages, a new chapter on the nef-partition is added

Scientific paper

In this note we study several conditions to be imposed on a mirror symmetry candidate to the generic multi-quasihomogeneous Calabi-Yau variety defined in the product of the quasihomogeneous projective spaces. We propose several properties for a Calabi-Yau complete intersection variety so that its period integrals can be expressed by means of quasihomogeneous weights of its mirror symmetry candidate as it has been suggested by Berglund, Candelas et altri. As a corollary, we see certain duality between the monodromy data and the Poincar\'e polynomials of the Euler characteristic for the pairs of our varieties.

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