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008			040520s2004 enk b 00100 eng
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020			_a0521547741
040			_aDLC _cDLC _dOCL _dUBA _dBAKER _dNOR
049			_aNORA
050	0	0	_aQA614.58 _b.W35 2004
060			_bWS
082	0	0	_a512.22 _222
084			_a512.22 _bWS
090			_aQA614.58 _i.W45 2004
100	1		_aWall, C. T. C. _q(Charles Terence Clegg).)
245	1	0	_aSingular points of plane curves _h[[Book] /] _cC.T.C. Wall.
250			_a1st.
260			_aCambridge, UK ; _aNew York : _bCambridge University Press, _cc2004.
300			_axi, 370 p. ; _c24 cm.
440		0	_aLondon Mathematical Society student texts ; _v63
504			_aIncludes bibliographical references (p. 357-367) and index.
505	0	0	_tPreface -- _g1. _tPreliminaries -- _g2. _tPuiseux' theorem -- _g3. _tResolutions -- _g4. _tContact of two branches -- _g5. _tTopology of the singularity link -- _g6. The. _tMilnor fibration -- _g7. _tProjective curves and their duals -- _g8. _tCombinatorics on a resolution tree -- _g9. _tDecomposition of the link complement and the Milnor fibre -- _g10. The. _tmonodromy and the Seifert form -- _g11. _tIdeals and clusters -- _tReferences -- _tIndex.
520			_aThe simplest singularities of a plane curve are self-crossings and cusps. Equivalence of singular points of (complex) plane curves can be defined using combinatorial data, resolution data or topological data; all give the same result. The first half of this book, which is based on a M.Sc. Course, works up to this synthesis via Puiseux series (parametrising the curve), resolution of singularities, infintely near points and the Alexander polynomial. For curves in the projective plane, formulae for the genus and the class depend on the singularities. The topology gives a fibration (due to Minor), described by the monodromy self-map of the fibre, a compact surface. The monodromy is approached through resolution trees, the group of exceptional cycles, combinatorial data, and the decomposition theorems of Thurston and of Jaco-Shalen-Johannsen. The author obtains a criterion for the monodromy to be (setwise) finite and a close relation between the Eggers tree, the resolution graph and the Eisenbud-Neumann diagram. Ahe calculates the characteristic polynomials of the monodromy, studies the Seifert form, and calculates the signatures that determine it over the reals. Ideals in the local ring of appoint are related to the cycles studied earlier, and (by a Galois correspondence) with the clusters of Enriques; this involves valuative and integral closure. This graduate text gives an introduction to this attractive area of mathematics. By synthesizing different perspectives it offers a novel view and a number of new results. Exercises and suggestions for further rreading are included. - Back cover.
521			_aAll Ages.
650		0	_aSingularities (Mathematics) _vCongresses.
650		0	_aCurves, Plane _vCongresses.
700	1		_aWall, C. T. C.
949			_a30205003234787
994			_a02 _bNOR
001			0000024649
003			0000
942			_cBK
999			_c52320 _d52320