The set of destabilizing curves for deformed Hermitian Yang-Mills and Z-critical equations on surfaces

Autor:	Khalid, Sohaib, Dyrefelt, Zakarias Sjöström
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry Mathematics - Algebraic Geometry 14J60 32Q26 53C07 53C55 53E30
Druh dokumentu:	Working Paper
Popis:	We show that on any compact K\"ahler 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. Comment: accepted version, to appear in Int. Math. Res. Not. (IMRN); details about wall structure added in Corollary 1.7, Proposition 3.17, Remark 3.18
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.06374 Zobrazit plný text záznamu View this record from Arxiv