000			03665nam a22003618i 4500
001			CR9780511569326
003			UkCbUP
005			20200124160236.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090520s2000||||enk o ||1 0|eng|d
020			_a9780511569326 (ebook)
020			_z9780521789592 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA565 _b.C37 2000
082	0	0	_a516.3/5 _221
100	1		_aCasas-Alvero, E. _q(Eduardo), _d1948- _eauthor.
245	1	0	_aSingularities of plane curves / _cEduardo Casas-Alvero.
264		1	_aCambridge : _bCambridge University Press, _c2000.
300			_a1 online resource (xv, 345 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v276
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_tProjective spaces -- _tPower series -- _tSurfaces, local coordinates -- _tMorphisms -- _tLocal rings -- _tTangent and cotangent spaces -- _tCurves -- _tGerms of curves -- _tMultiplicity and tangent cone -- _tSmooth germs -- _tExamples of singular germs -- _tNewton--Puiseux algorithm -- _tNewton polygon -- _tFractionary power series -- _tSearch for y-roots of f(x, y) -- _tThe Newton-Puiseux algorithm -- _tPuiseux theorem -- _tSeparation of y-roots -- _tThe case of convergent series -- _tAlgebraic properties of C{x, y} -- _tFirst local properties of plane curves -- _tThe branches of a germ -- _tThe Puiseux series of a germ -- _tPoints on curves around O -- _tLocal rings of germs -- _tParameterizing branches -- _tIntersection multiplicity -- _tPencils and linear systems -- _tInfinitely near points -- _tBlowing up -- _tTransforming curves and germs -- _tInfinitely near points -- _tEnriques' definition of infinitely near points -- _tProximity -- _tFree and satellite points -- _tResolution of singularities -- _tEquisingularity -- _tEnriques diagrams -- _tThe ring in the first neighbourhood -- _tThe rings in the successive neighbourhoods -- _tArtin theorem for plane curves -- _tVirtual multiplicities -- _tCurves through a weighted cluster -- _tWhen virtual multiplicities are effective -- _tBlowing up all points in a cluster -- _tExceptional divisors and dual graphs -- _tThe totla transform of a curve -- _tUnloading -- _tThe number of conditions -- _tAdjoint germs and curves -- _tNoether's Af + B[phi] theorem -- _tAnalysis of branches -- _tCharacteristic exponents -- _tThe first characteristic exponent.
520			_aThis book provides a comprehensive and self-contained exposition of the algebro-geometric theory of singularities of plane curves, covering both its classical and its modern aspects. The book gives a unified treatment, with complete proofs, presenting modern results which have only ever appeared in research papers. It updates and correctly proves a number of important classical results for which there was formerly no suitable reference, and includes new, previously unpublished results as well as applications to algebra and algebraic geometry. This book will be useful as a reference text for researchers in the field. It is also suitable as a textbook for postgraduate courses on singularities, or as a supplementary text for courses on algebraic geometry (algebraic curves) or commutative algebra (valuations, complete ideals).
650		0	_aCurves, Plane.
650		0	_aSingularities (Mathematics)
776	0	8	_iPrint version: _z9780521789592
830		0	_aLondon Mathematical Society lecture note series ; _v276.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511569326
999			_c518066 _d518064