Algebraic Geometry and Singularities [Paperback]

I Resolution of Singularities.- D?singularisation en dimension 3 et caract?ristique p.- 1 Diff?rentes notions de d?singularisation.- 2 Premi?re r?duction.- 3 Deuxi?me r?duction, construction dun mod?le projectif.- 4 Troisi?me r?duction, birationnel devient projectif.- 5 Final: Morphisme projectif birationnel devient d?singularisation.- Sur lespace des courbes trac?es sur une singularit?.- 1 Introduction.- 2 Structure pro-alg?brique de Tespace des courbes et la fonction de M. Art in dune singularit?.- 3 Families de courbes (selon J. Nash) et d?singularisations.- 4 Courbes sur une singularit? isol?e dhypersurface.- 5 Courbes lisses sur une singularit? de surface.- 6 Deux exemples.- Blowing up acyclic graphs and geometrical configurations.- 1 Introduction.- 2 Basic concepts and notations.- 3 Blowing up acyclic graphs.- 4 Graphic representation of the blowing up for a geometric configuration.- 5 Geometric modification for acyclic graphs.- On a Newton polygon approach to the uniformization of singularities of characteristic p.- 1 Introduction.- 2 Newton polygon and uniformization for ?1 ? n ? 1.- 3 Jumping lemma and Uniformization for ?1 = n ? 2.- 4 The classification of 3-dimensional singularities and uniformization for ?2 ? 3 or ?2 = $${\pi _{\mathop 2\limits^ * }} \geqslant 2$$.- 5 Uniformization for ?2 = 2 and $${\pi _{\mathop 2\limits^ * }}$$ = 1.- 6 Uniformization for ?2 = 1.- Geometry of plane curves via toroidal resolution.- 1 Introduction.- 2 Toric blowing-up and a tower of toric blowing-ups.- 3 Dual Newton diagram and an admissible toric blowing-up.- 4 Resolution complexity.- 5 Characteristic power and Puiseux Pairs.- 6 The Puiseux pairs of normal slice curves.- 7 Geometry of plane curves via a toroidal resolution.- 8 Iterated generic hyperplane section curves.- to the algorithm of resolution.- 1 Introduction.- 2 Stating the problem of resolution of singularities.- 3 Auxiliary result: Idealistic pairs.- 4 Constructive resolutions.- 5 The language of grovel3‚