TY - BOOK ID - 207277 TI - Introduction to Plane Algebraic Curves PY - 2005 SN - 0817644431 0817643818 PB - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, DB - UniCat KW - Curves, Plane. KW - Curves, Algebraic. KW - Singularities (Mathematics) KW - Algebraic curves KW - Algebraic varieties KW - Higher plane curves KW - Plane curves KW - Geometry, Algebraic KW - Algebraic geometry KW - Geometry, algebraic. KW - Algebraic topology. KW - Mathematics. KW - Algebra. KW - Field theory (Physics). KW - Algebraic Geometry. KW - Algebraic Topology. KW - Applications of Mathematics. KW - Commutative Rings and Algebras. KW - Associative Rings and Algebras. KW - Field Theory and Polynomials. KW - Geometry KW - Classical field theory KW - Continuum physics KW - Physics KW - Continuum mechanics KW - Mathematics KW - Mathematical analysis KW - Math KW - Science KW - Topology KW - Algebraic geometry. KW - Applied mathematics. KW - Engineering mathematics. KW - Commutative algebra. KW - Commutative rings. KW - Associative rings. KW - Rings (Algebra). KW - Algebra KW - Engineering KW - Engineering analysis KW - Algebraic rings KW - Ring theory KW - Algebraic fields KW - Rings (Algebra) KW - Geometry, Algebraic. KW - Field theory (Physics) UR - https://www.unicat.be/uniCat?func=search&query=sysid:207277 AB - This 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 . ER -