Twisted Adiabatic Limit for Complex Structures
Twisted Adiabatic Limit for Complex Structures
Given a complex manifold $X$ and a smooth positive function $\eta$ thereon, we perturb the standard differential operator $d=\partial + \bar\partial$ acting on differential forms to a first-order differential operator $D_\eta$ whose principal part is $\eta\partial + \bar\partial$. The role of the zero-th order part is to force the integrability …