We construct Bridgeland stability conditions on the derived category of smooth quasiprojective Deligne-Mumford surfaces whose coarse moduli spaces have ADE singularities. This unifies the construction for smooth surfaces and Bridgeland's work on Kleinian singularities. The construction hinges on an orbifold version of the Bogomolov-Gieseker inequality for slope semistable sheaves on the stack, and makes use of the Toën-Hirzebruch-Riemann-Roch theorem.

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We give a computer-free proof that the Mathieu group M 22 is a homomorphic image of the progenitor 2 ⋆14 : L 3 (2) factorized by three relations.

Suppose f, g are homogeneous polynomials of degree d defining smooth hypersurfaces X f = V (f ) ⊂ P m−1 and Xg = V (g) ⊂ P n−1 . Then the sum of f and g defines a smooth hypersurface X = V (f ⊕ g) ⊂ P m+n−1 with an action of µ d scaling the g variables. Motivated by the work of Orlov, we construct a semi-orthogonal decomposition of the derived category of coherent sheaves on [X/µ d ] provided d ≥ max{m, n}.

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