Let C be a complex integral curve with plannar singularities. Let J be the compactified Jacobian of C. There are two filtrations on the cohomology group H∗(J). One is obtained by the nilpotent morphism defined by cupping a certain ample divisor on J
Nearby in the stack
, which we call the Lefschetz filtration. To obtain the other filtration, we put
C
into a family of curves
C→B
so that
J
can be embedded into a family
f:J→B
, and we let
B,C,J
be smooth. Then
Rf∗(QJ)
decomposes into a direct sum of its (shifted) perverse cohomologies. Restricting this decomposition to fibers, we get a filtration on
H∗(J)
called the perverse filtration. We show in this paper that these two filtrations are opposite to each other as conjectured by Maulik-Yun.