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.
Rocky Mountain J. Math.
50(5):
1599-1616
(October 2020).
DOI: 10.1216/rmj.2020.50.1599
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