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  "body": "\n## Summary\n\nThe characteristic variety of a linear differential operator is the set of points and nonzero covectors where its [[principal symbol|F31T650DKY]] vanishes.\nA hypersurface whose normal never lies in this set is called noncharacteristic, and the Cauchy problem with data on such a hypersurface is well behaved.\nIn algebraic analysis the same idea defines the characteristic variety of a D-module.\nSee the [[definition|JMJEVS7S1V]].\n\n## Explanations\n\n### L1 human\n\nThe characteristic variety lists the directions in which an operator fails to control the highest derivatives.\nAlong such directions, data on a surface do not determine how the solution leaves the surface.\nFor the [[wave equation|5EHD2XBQDG]] $\\partial_t^2 u - \\partial_x^2 u$, the symbol $\\tau^2 - \\xi^2$ vanishes when $\\tau = \\pm \\xi$.\nThe corresponding curves $x \\pm t = \\text{const}$ are the light rays along which waves travel.\n",
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