By Vincent Cossart (auth.), Antonio Campillo López, Luis Narváez Macarro (eds.)

The concentration of this quantity lies on singularity concept in algebraic geometry. It contains papers documenting contemporary and unique advancements and strategies in topics equivalent to solution of singularities, D-module concept, singularities of maps and geometry of curves. The papers originate from the 3rd overseas convention on Algebraic Geometry held in l. a. Rábida, Spain, in December 1991. when you consider that then, the articles have passed through a meticulous means of refereeing and development, and so they were geared up right into a finished account of the cutting-edge during this field.

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Algebraic approximation of structures over complete local rings. Pub!. Math. IHES 36 1969 pp23-58 [2] Artin M. ies of surfaces. Ann. 88 1966 pp129-136 [3] Bouvier C. et Gonzalez-Sprinberg G. G-desingularisations de varietes toriques. C. R. Acad. Sci. Paris Ser. I :\:lath. a paraitre. [4] Campillo A. et Castellanos J. Arf closure relative to a divisorial valuation and transversal curves. PrepubL Dep. de Algebra, Geometria y Topologia, Univ. Valladolid, n 11 a paraitre. [5] Gonzalez-Sprinberg G. et Lejeune-Jalabert j\tl.

Y») E G' . The morphisms which take maximal points to maximal points will be called dominant. ransitive if for any pair of arcs (x, y), (y, z) with x i- z, then (x, z) is also an arc. , if (x, y) and (y, x) are not both in G for x i- y. A transitive graph is acyclic if and only if it is antisymmetric, and an acyclic transitive graph (X, G) has a partial ordering (X, :::;) where x < y if and only if (x, y) E G. s a path Xl ... x q , q ~ 2, with Xl = x and Xq = y}. Example 2-1. s (XI,G I ) and (X2 ,G2 ).

La suite des multiplicites de 1\ash m = (mo, ... , m;, ... ) de h E 1t se calcule facilement par la formule recurrente suivante : ° mo + ... 1) hEe(h,i) ou C(h, i) := {k E C I PiCk) = Pi(h)}. Autrement dit, c'est Ie minimum des multiplicites d'intersection locale en de l'hypersurface V avec une courbe tracee sur son espace ambiant (kn, 0) dont Ie i-erne jet coincide avec celui de h. 1) qu'on a aussi : Proposition 4-3. Soit r h : (T,o) ---- (V x T,O x 0) =: (n'o,Oo) 1e graphe de h E 1t et soit : ° 1a suite de marphismes telle que 1.