On the stack of 0‐dimensional coherent sheaves: Motivic aspects

Abstract Let be a variety. In this survey, we study (decompositions of) the motivic class, in the Grothendieck ring of stacks, of the stack of 0‐dimensional coherent sheaves of length on . To do so, we review the construction of the support map to the symmetric product and we prove that, for any closed point , the motive of the punctual stack parametrising sheaves supported at only depends on a formal neighbourhood of . We perform the same analysis for the Quot‐to‐Chow morphism , for a fixed sheaf .