000			02233 a2200241 4500
008			211220b |||||||| |||| 00| 0 eng d
020			_a9783540586579
082			_a516.35 _bMUM
100			_aMumford, David
245			_aAlgebraic geometry I: complex projective varieties
260			_bSpringer - Verlag, _c1995 _aBerlin:
300			_ax, 186p. ; _bpb, _c23 cm.
365			_aEURO _b54.99
440			_aClassics in Mathematics
504			_aIncludes index
520			_aLet me begin with a little history. In the 20th century, algebraic geometry has gone through at least 3 distinct phases. In the period 1900-1930, largely under the leadership of the 3 Italians, Castelnuovo, Enriques and Severi, the subject grew immensely. In particular, what the late 19th century had done for curves, this period did for surfaces: a deep and systematic theory of surfaces was created. Moreover, the links between the "synthetic" or purely "algebro-geometric" techniques for studying surfaces, and the topological and analytic techniques were thoroughly explored. However the very diversity of tools available and the richness of the intuitively appealing geometric picture that was built up, led this school into short-cutting the fine details of all proofs and ignoring at times the time­ consuming analysis of special cases (e. g. , possibly degenerate configurations in a construction). This is the traditional difficulty of geometry, from High School Euclidean geometry on up. In the period 1930-1960, under the leadership of Zariski, Weil, and (towards the end) Grothendieck, an immense program was launched to introduce systematically the tools of commutative algebra into algebraic geometry and to find a common language in which to talk, for instance, of projective varieties over characteristic p fields as well as over the complex numbers. In fact, the goal, which really goes back to Kronecker, was to create a "geometry" incorporating at least formally arithmetic as well as projective geo­ metry.
650			_aMathematics
650			_aAlgebraic varieties
650			_aGeometry - Algebraic
650			_aTopological and analytic techniques
650			_aCommutative algebra - Algebraic geometry
942			_2ddc _cTD
999			_c55963 _d55963