Curvature of higher direct image sheaves

2015/01/28 by Geiger, Thomas, Schumacher, Georg
#14D20 #32L10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1501.07070

Abstract

Given a family (F,h) → X × S of Hermite-Einstein bundles on a compact Kähler manifold (X,g) we consider the higher direct image sheaves R^q p_* O(F) on S, where p: X × S → S is the projection. On the complement of an analytic subset these sheaves are locally free and carry a natural metric, induced by the L₂ 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.

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