2011/06/12 by Shi-shyr Roan, Roan, Shi-shyr
Mathematics · Physics and Astronomy · #14N10 #2010: 14M25 #32J17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #hep-th #math.AG #msc:14M25 #msc:14N10 #msc:32J17
paper · pdf · doi:10.48550/arxiv.1106.2323
Latex 29 page
arxiv created 2011/06/12 · openalex publication_date 2011/06/12 · arxiv updated 2011/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive the combinatorial representations of Picard group and deformation space of anti-canonical hypersurfaces of a toric variety using techniques in toric geometry. The mirror cohomology correspondence in the context of mirror symmetry is established for a pair of Calabi-Yau (CY) \sf n-spaces in toric varieties defined by reflexive polytopes for an arbitrary dimension \sf n. We further identify the Kahler cone of the toric variety and degeneration cone of CY hypersurfaces, by which the Kahler cone and degeneration cone for a mirror CY pair are interchangeable under mirror symmetry. In particular, different degeneration cones of a CY 3-fold are corresponding to flops of its mirror 3-fold.