  In this paper, we introduce a new class of structured spaces which is locally
modeled by Costello's L-infinity spaces. This provides an alternative approach
to study the derived geometric structures in the algebraic, analytic, or smooth
category. Our main result asserts that on a compact complex manifold, the
moduli space of simple holomorphic structures on a complex vector bundle with a
fixed determinant bundle, admits a natural analytic homotopy L-infinity
enhancement.

Algebraic Geometry