000			03608nam a22004935i 4500
001			978-3-0348-0493-6
003			DE-He213
005			20140220083254.0
007			cr nn 008mamaa
008			120824s2012 sz | s |||| 0|eng d
020			_a9783034804936 _9978-3-0348-0493-6
024	7		_a10.1007/978-3-0348-0493-6 _2doi
050		4	_aQA564-609
072		7	_aPBMW _2bicssc
072		7	_aMAT012010 _2bisacsh
082	0	4	_a516.35 _223
100	1		_aBrieskorn, Egbert. _eauthor.
245	1	0	_aPlane Algebraic Curves _h[electronic resource] : _bTranslated by John Stillwell / _cby Egbert Brieskorn, Horst Knörrer.
264		1	_aBasel : _bSpringer Basel : _bImprint: Birkhäuser, _c2012.
300			_aX, 721 p. 301 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aModern Birkhäuser Classics
505	0		_aI. History of algebraic curves -- 1. Origin and generation of curves -- 2. Synthetic and analytic geometry -- 3. The development of projective geometry -- II. Investigation of curves by elementary algebraic methods -- 4. Polynomials -- 5. Definition and elementary properties of plane algebraic curves -- 6. The intersection of plane curves -- 7. Some simple types of curves -- III. Investigation of curves by resolution of singularities -- 8. Local investigations -- 9. Global investigations -- Bibliography -- Index.
520			_aIn a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany, “Plane Algebraic Curves” reflects the author’s concern for the student audience through emphasis upon motivation, development of imagination, and understanding of basic ideas. As classical objects, curves may be viewed from many angles; this text provides a foundation for the comprehension and exploration of modern work on singularities.   ---   In the first chapter one finds many special curves with very attractive geometric presentations – the wealth of illustrations is a distinctive characteristic of this book – and an introduction to projective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezout’s theorem and a detailed discussion of cubics. The heart of this book – and how else could it be with the first author – is the chapter on the resolution of singularities (always over the complex numbers).  (…) Especially remarkable is the outlook to further work on the topics discussed, with numerous references to the literature. Many examples round off this successful representation of a classical and yet still very much alive subject. (Mathematical Reviews)
650		0	_aMathematics.
650		0	_aGeometry, algebraic.
650		0	_aAlgebra.
650		0	_aAlgebraic topology.
650	1	4	_aMathematics.
650	2	4	_aAlgebraic Geometry.
650	2	4	_aCommutative Rings and Algebras.
650	2	4	_aAlgebraic Topology.
700	1		_aKnörrer, Horst. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783034804929
830		0	_aModern Birkhäuser Classics
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-0348-0493-6
912			_aZDB-2-SMA
999			_c101752 _d101752