2015/06/24 by Andrew Schaug, Schaug, Andrew
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AG #math.SG
paper · pdf · doi:10.48550/arxiv.1506.07226
45 pages, 1 figure
arxiv created 2015/06/24 · openalex publication_date 2015/06/24 · arxiv updated 2015/06/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In the early 1990s, Borcea-Voisin orbifolds were some of the ear- liest examples of Calabi-Yau threefolds shown to exhibit mirror symmetry. However, their quantum theory has been poorly investigated. We study this in the context of the gauged linear sigma model, which in their case encom- passes Gromov-Witten theory and its three companions (FJRW theory and two mixed theories). For certain Borcea-Voisin orbifolds of Fermat type, we calculate all four genus zero theories explicitly. Furthermore, we relate the I-functions of these theories by analytic continuation and symplectic transfor- mation. In particular, the relation between the Gromov-Witten and FJRW theories can be viewed as an example of the Landau-Ginzburg/Calabi-Yau correspondence for complete intersections of toric varieties.