A resolution of singularities of Drinfeld compactification with an Iwahori structure

The Drinfeld compactification Bun ¯ B ′ {Bun}B’ of the moduli stack Bun B ′ BunB’ of Borel bundles on a curve X X with an Iwahori structure is important in the geometric Langlands program. It is closely related to the study of representation theory. In this paper, we construct a resolution of singularities of it using a modification of Justin Campbell’s construction of the Kontsevich compactification. Furthermore, the moduli stack Bun B ′ {Bun}B’ admits a stratification indexed by the Weyl group. For each stratum, we construct a resolution of singularities of its closure. Then we use this resolution of singularities to prove a universally local acyclicity property, which is useful in the quantum local Langlands program.