Perverse Curves and Mirror Symmetry
arXiv:1309.1803 · doi:10.1090/jag/666
Abstract
This work establishes a subtle connection between mirror symmetry for Calabi-Yau threefolds and that of curves of higher genus. The linking structure is what we call a perverse curve. We show how to obtain such from Calabi-Yau threefolds in the Batyrev mirror construction and prove that their Hodge diamonds are related by the mirror duality.
24 pages, 6 figures, to appear in J. Algebraic Geom