Given a locally free sheaf on a projective space , a natural question is to compute the -cohomology of its restriction to an affine subspace equipped with a flat Kähler form . This problem arises naturally when studying the geometry of moduli of monads. We identify the known construction of a natural hermitian structure on the moduli space of the associated vector bundles with the Weil–Petersson approach to a Kähler metric based on harmonic theory for Kodaira–Spencer tensors. We show that for a holomorphic family of monads on or on a modification of , there is a Kodaira–Spencer map providing the base with a Kähler structure.
"$L^2$-cohomology for affine spaces and an application to monads." Rocky Mountain J. Math. 50 (5) 1599 - 1616, October 2020. https://doi.org/10.1216/rmj.2020.50.1599