000			04171nam a22004935i 4500
001			978-0-8176-4443-7
003			DE-He213
005			20251006084434.0
007			cr nn 008mamaa
008			100301s2005 xxu| s |||| 0|eng d
020			_a9780817644437
020			_a99780817644437
024	7		_a10.1007/0-8176-4443-1 _2doi
082	0	4	_a512.44 _223
100	1		_aKunz, Ernst. _eauthor.
245	1	0	_aIntroduction to Plane Algebraic Curves _h[electronic resource] / _cby Ernst Kunz.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2005.
300			_aXII, 293 p. 52 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPlane Algebraic Curves -- Ane 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.
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 * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook From a review of the German edition: "[T]he reader is invited to learn some topics from commutative ring theory by mainly studying their illustrations and applications in plane curve theory. This methodical approach is certainly very enlightening and efficient for both teachers and students... The whole text is a real masterpiece of clarity, rigor, comprehension, methodical skill, algebraic and geometric motivation...highly enlightening, motivating and entertaining at the same time... One simply cannot do better in writing such a textbook." -Zentralblatt MATH
650		0	_aMATHEMATICS.
650		0	_aGEOMETRY, ALGEBRAIC.
650		0	_aALGEBRA.
650		0	_aFIELD THEORY (PHYSICS).
650		0	_aALGEBRAIC TOPOLOGY.
650	1	4	_aMATHEMATICS.
650	2	4	_aCOMMUTATIVE RINGS AND ALGEBRAS.
650	2	4	_aALGEBRAIC GEOMETRY.
650	2	4	_aASSOCIATIVE RINGS AND ALGEBRAS.
650	2	4	_aALGEBRAIC TOPOLOGY.
650	2	4	_aFIELD THEORY AND POLYNOMIALS.
650	2	4	_aAPPLICATIONS OF MATHEMATICS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817643812
856	4	0	_uhttp://dx.doi.org/10.1007/0-8176-4443-1 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59641 _d59641