Let be a variety over a field and let be its space of arcs. We study the complete local ring , where is the stable point defined by an integer and a divisorial valuation on . Assuming char , we prove that embdim , where is the Mather discrepancy of with respect to . We also obtain that dim has as lower bound , where is the Mather–Jacobian log-discrepancy of with respect to . For normal and a complete intersection, we prove as a consequence that if has codimension 1 in then the discrepancy .
Cite this article
Hussein Mourtada, Ana J. Reguera, Mather Discrepancy as an Embedding Dimension in the Space of Arcs. Publ. Res. Inst. Math. Sci. 54 (2018), no. 1, pp. 105–139DOI 10.4171/PRIMS/54-1-4