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October 2020 $L^2$-cohomology for affine spaces and an application to monads
Nicholas P. Buchdahl, Georg Schumacher
Rocky Mountain J. Math. 50(5): 1599-1616 (October 2020). DOI: 10.1216/rmj.2020.50.1599

Abstract

Given a locally free sheaf on a projective space n, a natural question is to compute the L2-cohomology of its restriction to an affine subspace n=nn1 equipped with a flat Kähler form ωn. 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 2 or on a modification ˜2 of 2, there is a Kodaira–Spencer map providing the base with a Kähler structure.

Citation

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Nicholas P. Buchdahl. Georg Schumacher. "$L^2$-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

Information

Received: 14 July 2019; Revised: 23 February 2020; Accepted: 3 March 2020; Published: October 2020
First available in Project Euclid: 5 November 2020

zbMATH: 07274822
MathSciNet: MR4170674
Digital Object Identifier: 10.1216/rmj.2020.50.1599

Subjects:
Primary: 14J60, 32G13, 53C07

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 5 • October 2020
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