The Set of Destabilizing Curves for Deformed Hermitian Yang–Mills and Z-Critical Equations on Surfaces

TY - JOUR

T1 - The Set of Destabilizing Curves for Deformed Hermitian Yang–Mills and Z-Critical Equations on Surfaces

AU - Khalid, Sohaib

AU - Dyrefelt, Zakarias Sjöström

N1 - Publisher Copyright: © The Author(s) 2023. Published by Oxford University Press. All rights reserved.

PY - 2024/4

Y1 - 2024/4

N2 - We show that on any compact Kähler surface existence of solutions to the Z-critical equation can be characterized using a finite number of effective conditions, where the number of conditions is bounded above by the Picard number of the surface. This leads to a first PDE analogue of the locally finite wall-chamber decomposition in Bridgeland stability. As an application we characterize optimally destabilizing curves for Donaldson’s J-equation and the deformed Hermitian Yang–Mills equation, prove a non-existence result for optimally destabilizing test configurations for uniform J-stability, and remark on improvements to convergence results for certain geometric flows.

AB - We show that on any compact Kähler surface existence of solutions to the Z-critical equation can be characterized using a finite number of effective conditions, where the number of conditions is bounded above by the Picard number of the surface. This leads to a first PDE analogue of the locally finite wall-chamber decomposition in Bridgeland stability. As an application we characterize optimally destabilizing curves for Donaldson’s J-equation and the deformed Hermitian Yang–Mills equation, prove a non-existence result for optimally destabilizing test configurations for uniform J-stability, and remark on improvements to convergence results for certain geometric flows.

U2 - 10.1093/imrn/rnad256

DO - 10.1093/imrn/rnad256

M3 - Journal article

AN - SCOPUS:85180569505

SN - 1073-7928

VL - 2024

SP - 5773

EP - 5814

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 7

ER -