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Mather discrepancy and the arc spaces. (Discrépance de Mather et les espaces d’arcs.) (English. French summary) Zbl 1360.14048
Ann. Inst. Fourier 63, No. 1, 89-111 (2013); corrigendum ibid. 67, No. 4, 1609-1612 (2017).
Summary: A goal of this paper is a characterization of singularities according to a new invariant, Mather discrepancy. We also show some evidences convincing us that Mather discrepancy is a reasonable invariant in a view point of birational geometry.

MSC:
14E18 Arcs and motivic integration
14B05 Singularities in algebraic geometry
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