Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties
Lev Borisov
TL;DR
This paper introduces a combinatorial duality for lattice polyhedra that aims to generate mirror symmetric pairs of Calabi-Yau complete intersections within Gorenstein toric Fano varieties, extending Batyrev's hypersurface duality.
Contribution
It generalizes Batyrev's polar duality to Calabi-Yau complete intersections, providing a new combinatorial framework for mirror symmetry in Gorenstein toric Fano varieties.
Findings
Proposes a conjectural duality for lattice polyhedra.
Suggests a new method to construct mirror pairs of Calabi-Yau varieties.
Extends the scope of mirror symmetry beyond hypersurfaces.
Abstract
We propose a combinatorical duality for lattice polyhedra which conjecturally gives rise to the pairs of mirror symmetric families of Calabi-Yau complete intersections in toric Fano varieties with Gorenstein singularities. Our construction is a generalization of the polar duality proposed by Batyrev for the case of hypersurfaces.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Combinatorial Mathematics · Geometry and complex manifolds