000			02003 a2200241 4500
999			_c54399 _d54399
008			210323b ||||| |||| 00| 0 eng d
020			_a9780521108478
082			_a516.5 _bPES
100			_aPeskine, Christian
245			_aAlgebraic introduction to complex projective geometry, Vol. 1
260			_bCambridge University Press, _c2009. _aCambridge:
300			_ax, 230p. : ill. ; _bpb; _c24 cm.
365			_aGBP _b42.99
440			_aCambridge studies in advanced mathematics ; 47
504			_aIncludes bibliographical references and index.
520			_aIn this introduction to commutative algebra, the author leads the beginning student through the essential ideas, without getting embroiled in technicalities. The route chosen takes the reader quickly to the fundamental concepts for understanding complex projective geometry, the only prerequisites being a basic knowledge of linear and multilinear algebra and some elementary group theory. In the first part, the general theory of Noetherian rings and modules is developed. A certain amount of homological algebra is included, and rings and modules of fractions are emphasised, as preparation for working with sheaves. In the second part, the central objects are polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalisation lemma and Hilbert's Nullstellensatz, affine complex schemes and their morphisms are introduced; Zariski's main theorem and Chevalley's semi-continuity theorem are then proved. Finally, a detailed study of Weil and Cartier divisors provides a solid background for modern intersection theory. This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra.
650			_aFunctions of complex variables
650			_aGeometry, Algebraic
650			_aGeometry, Projective
650			_aNoetherian rings and modules
650			_aMorphisms of affine schemes
942			_2ddc _cTD