Landau–Ginzburg models of complete intersections in Lagrangian Grassmannians

Abstract

Let LG(n) be the Lagrangian Grassmannian parameterizing the Lagrangian linear subspaces of the 2n-dimensional complex symplectic vector space. It has a Plücker embedding to a projective space P, so that for H = OP(1) we have Pic(LG(n)) = ZH. Let X ⊂ LG(n) be a smooth Fano complete intersection of degrees d1, . . . , dk. We have ∑k i=1 di < n + 1, and dk+1 = n + 1 − ∑k i=1 di is the Fano index of X. Let pi, i = 1, . . . , n, be formal variables. Consider the series