TL;DR
This paper explores a novel link between mirror symmetry in Calabi-Yau threefolds and higher genus curves through the concept of perverse curves, demonstrating their Hodge diamonds are mirror duals.
Contribution
It introduces the concept of perverse curves and shows how they relate mirror symmetry properties of Calabi-Yau threefolds to higher genus curves.
Findings
Perverse curves can be derived from Calabi-Yau threefolds in Batyrev's mirror construction.
Hodge diamonds of these perverse curves are related by mirror duality.
The work establishes a new connection between mirror symmetry and higher genus curves.
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.
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