Riemann--Roch duality for the marked rank second difference

The four affine terms in graph Riemann--Roch cancel in the marked second difference. Consequently rankDelta is invariant under the involution D ↦ K + u + v - D.

theorem Bananas.rankDelta_canonical_dual (M : TwiceMarked) (hconn : graphConnected M.graph) (D : CFDiv M.graph) : rankDelta M D = rankDelta M (canonicalDivisor M.graph + oneChip M.u + oneChip M.v - D)

Riemann--Roch preserves the marked rank second difference after translating the canonical complement by the two marked chips.