The combinatorics of Lehn’s conjecture

Lehn’s conjecture. The number of (n− 2)-subspaces in P2n−2 which are n-secant to a smooth curve, C ⊂ P2n−2, of genus g and degree d is a classical enumerative calculation [ACGH]. The answer can be expressed in terms of Segre integrals over the symmetric product C [n] of C. Let the line bundle H → C be the degree d restriction of OP2n−2(1). The n-secant problem is solved by the Segre integral, and the answer can be written in closed form [LeB], [C],