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  "body": "\n## Summary\n\nA stability condition on a [[triangulated category|T2V7GJJ2EN]] is a pair made of a central charge and a slicing.\nThe central charge is a homomorphism from the Grothendieck group to $\\C$.\nThe slicing assigns to each real number a class of semistable objects of that phase.\nThe notion was introduced by Tom Bridgeland to give a uniform meaning to stability of sheaves and of quiver representations.\nThe stability conditions on a fixed category form a space with a natural topology.\nThe study of this space links algebraic geometry with string theory and mirror symmetry.\n\n## Explanations\n\n### L1 human\n\nA stability condition gives each object of a category a complex number, its central charge, which records a kind of mass and an angle.\nThe angle, divided by $\\pi$, is called the phase.\nThe semistable objects are the basic building blocks, and every object splits in a unique way into layers of semistable pieces whose phases decrease.\nFor a smooth projective curve, the charge $Z(E) = -\\deg E + i \\operatorname{rk} E$ of a coherent sheaf $E$ recovers the classical slope stability of vector bundles.\nEach stability condition has a heart, which is the heart of a bounded [[t-structure|2GD9V7SA0E]], so it refines the choice of a t-structure.\n",
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