000			03425cam a22002654a 4500
001			vtls000001776
003			VRT
005			20250102223525.0
008			081109s2005 maua |b 001 0 eng
020			_a0817643818 (alk. paper)
039		9	_a201402040053 _bVLOAD _c201007310934 _dmalmash _c200811101350 _dvenkatrajand _c200811091429 _dNoora _y200811091428 _zNoora
050	0	0	_aQA567 _b.K8613 2005
100	1		_aKunz, Ernst, _d1933- _925104
240	1	0	_aEbene algebraische Kurven. _lEnglish
245	1	0	_aIntroduction to Plane Algebraic Curves / _cErnst Kunz ; translated by Richard G. Belshoff.
260			_aBoston : _bBirkhauser, _cc2005.
300			_axii, 293 p. : _bill. ; _c24 cm.
504			_aIncludes bibliographical references (p. [285]-287) and index.
505			_a* Preface * Conventions and Notation * Part I: Plane Algebraic Curves * Affine Algebraic Curves * Projective Algebraic Curves * The Coordinate Ring of an Algebraic Curve and the Intersections of Two Curves * Rational Functions on Algebraic Curves * Intersection Multiplicity and Intersection Cycle of Two Curves * Regular and Singular Points of Algebraic Curves. Tangents * More on Intersection Theory. Applications * Rational Maps. Parametric Representations of Curves * Polars and Hessians of Algebraic Curves * Elliptic Curves * Residue Calculus * Applications of Residue Theory to Curves * The Riemann--Roch Theorem * The Genus of an Algebraic Curve and of its Function Field * The Canonical Divisor Class * The Branches of a Curve Singularity * Conductor and Value Semigroup of a Curve Singularity * Part II: Algebraic Foundations * Algebraic Foundations * Graded Algebras and Modules * Filtered Algebras * Rings of Quotients. Localization * The Chinese Remainder Theorem * Noetherian Local Rings and Discrete Valuation Rings * Integral Ring Extensions * Tensor Products of Algebras * Traces * Ideal Quotients * Complete Rings. Completion * Tools for a Proof of the Riemann--Roch Theorem * References * Index * List of Symbols
520			_aThis work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the student only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed. Kunz's proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. The exposition focuses on the purely algebraic aspects of plane curve theory, leaving the topological and analytical viewpoints in the background, with only casual references to these subjects and suggestions for further reading. Most important to this text: emphasizes and utilizes the theory of filtered algebras, their graduated rings and Rees algebras, to deduce basic facts about the intersection theory of plane curves; presents residue theory in the affine plane and its applications to intersection theory; methods of proof for the Riemann-Roch theorem conform to the presentation of curve theory, formulated in the language of filtrations and associated graded rings; and examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook.
650		0	_aCurves, Plane. _925105
650		0	_aCurves, Algebraic. _925106
650		0	_aSingularities (Mathematics) _925107
942			_2lcc _n0 _cBK
999			_c10346 _d10346