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VOL. 74 | 2017 Curvature of higher direct image sheaves
Thomas Geiger, Georg Schumacher

Editor(s) Keiji Oguiso, Caucher Birkar, Shihoko Ishii, Shigeharu Takayama

Adv. Stud. Pure Math., 2017: 171-184 (2017) DOI: 10.2969/aspm/07410171


Given a family $(F,h) \to X \times S$ of Hermite-Einstein bundles on a compact Kähler manifold $(X,g)$ we consider the higher direct image sheaves $R^q p_* \mathcal{O}(F)$ on $S$, where $p: X \times S \to S$ is the projection. On the complement of an analytic subset these sheaves are locally free and carry a natural metric, induced by the $L_2$ inner product of harmonic forms on the fibers. We compute the curvature of this metric which has a simpler form for families with fixed determinant and families of endomorphism bundles. Furthermore, we discuss the metric for moduli spaces of stable vector bundles.


Published: 1 January 2017
First available in Project Euclid: 23 October 2018

zbMATH: 1392.32008
MathSciNet: MR3791213

Digital Object Identifier: 10.2969/aspm/07410171

Primary: 14D20 , 32L10

Keywords: Curvature of direct image sheaves , Families of Hermite-Einstein bundles , moduli spaces , Stable bundles , Weil-Petersson metric

Rights: Copyright © 2017 Mathematical Society of Japan


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