2020/11/16 by Elana Kalashnikov, Kalashnikov, Elana
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2011.08093
We introduce a superpotential for partial flag varieties of type A. This is a map W: Y^∘ → ℂ, where Y^∘ is the complement of an anticanonical divisor on a product of Grassmannians. The map W is expressed in terms of Plücker coordinates of the Grassmannian factors. This construction generalizes the Marsh--Rietsch Plücker coordinate mirror for Grassmannians. We show that in a distinguished cluster chart for Y, our superpotential agrees with earlier mirrors constructed by Eguchi--Hori--Xiong and Batyrev--Ciocan-Fontanine--Kim--van Straten. Our main tool is quantum Schubert calculus on the flag variety.