Blowing up Chern-Ricci flat balanced metrics

Abstract

Given a compact Chern-Ricci flat balanced orbifold, we show that its blow-up at a finite family of smooth points admits constant Chern scalar curvature balanced metrics, extending Arezzo-Pacard's construction to the balanced setting. Moreover, if the orbifold has isolated singularities and admits crepant resolutions, we show that they always carry Chern-Ricci flat balanced metrics, without any further hypothesis. In addition, we discuss the general constant Chern scalar curvature balanced case and discuss another version of the main Theorem assuming the existence of a special (n-2, n-2)-form. We also present several classes of examples in which our results can be applied.

40 pages, minor changes, published version

References in corpus (15)

• Geometric Model for Complex Non-Kaehler Manifolds with SU(3) Structure
• The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold
• Gauduchon metrics with prescribed volume form
• Solutions of the Strominger System via Stable Bundles on Calabi-Yau Threefolds
• Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients
• KAWA lecture notes on the Kähler-Ricci flow
• Special Hermitian metrics on compact solvmanifolds
• A Kummer construction for gravitational instantons
• Blowing up extremal Kähler manifolds II
• On Chern-Yamabe problem
• The Hermitian curvature flow on manifolds with non-negative Griffiths curvature
• A parabolic flow of balanced metrics
• Remarks on Chern-Einstein Hermitian metrics
• Extremal metrics on fibrations
• Dolbeault and Bott-Chern formalities: deformations and $\partial \overline{\partial }$-lemma