Mathematics – Algebraic Geometry
Scientific paper
2004-10-06
Bulletin de la SMF 134, no. 3 (2006), 383-394.
Mathematics
Algebraic Geometry
8 pages; compared to the first version, we changed slightly the title in order to make it similar with the title of math.AG/06
Scientific paper
Let (S,0) be a germ of complex analytic normal surface. On its minimal resolution, we consider the reduced exceptional divisor E and its irreducible components E_i. The Nash map associates to each irreducible component C_k of the space of arcs through 0 on S the unique component of E cut by the strict transform of the generic arc in C_k. Nash proved its injectivity and asked if it was bijective. As a particular case of our main theorem, we prove that this is the case if E.E_i <0 for any i.
Plenat Camille
Popescu-Pampu Patrick
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