Abstract
It is the purpose of this short note to give a global description of the cotangent sheaf of Grothendieck's Quot-scheme in terms of a relative Ext-sheaf of the universal subsheaf and the universal quotient sheaf. As an application one gets a description of the cotangent sheaf of the moduli space of stable sheaves in terms of a relative Ext-sheaf involving only a universal family in case such a family exists.
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