%0 Journal Article %T Perverse Curves and Mirror Symmetry %A Helge Ruddat %J Mathematics %D 2013 %I arXiv %X 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. %U http://arxiv.org/abs/1309.1803v2