2018/04/17 by Smith, Jack
#14M25 #53D37 #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1804.06386
Let X be a compact toric variety. The quantum cohomology of X decomposes as a direct sum, and associated to each summand Q is a toric fibre LQ with rank 1 local system. By building an explicit twisted-complex-like object, we show that on Q the Kodaira-Spencer isomorphism of Fukaya-Oh-Ohta-Ono factors through the closed-open string map to the Hochschild cohomology of LQ. We deduce that the latter is injective and hence, assuming an appropriate version of Abouzaid's criterion, that LQ split generates the corresponding summand of the Fukaya category.