Curvature of higher direct images of sheaves of twisted holomorphic forms

2024/07/05 by Young-Jun Choi, Choi, Young-Jun, Georg Schumacher +1
Mathematics · #14D20 #32G05 #32L10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic and Geometric Analysis #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.2407.04298

openalex publication_date 2024/07/05 · openalex created_date 2024/07/09 · openalex updated_date 2026/07/28

Abstract

This paper investigates the curvature properties of higher direct images R^qf_*Ω_X/S^p(E), where f: X→ S is a family of compact Kähler manifolds equipped with a hermitian vector bundle E → X. We derive a general curvature formula and explore several special cases, including those where p + q = n, q = 0, and p = n, with E being a line bundle. Furthermore, the paper examines the curvature in the context of fiberwise hermitian flat cases, families of Hermite-Einstein vector bundles, and applications to moduli spaces and Weil-Petersson metrics, providing some insight into their geometric and analytical properties.

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