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《代數麯麵(英文版)》是《Classics in Mathematics》係列之一，以現代觀點講述瞭代數幾何知識，將經典代數麯麵和現代代數麯麵有機結閤，很好地錶達齣瞭數學的整體性，是同時期很難得的一本代數麯麵教材。目次：奇點理論和奇點還原；麯綫的綫性係統；伴隨係和不變量理論；算術虧格和Riemann-Roch定理；連續非綫性係統；代數麯麵的拓撲性質；代數麯麵上的單積分和雙重積分；復平麵上的Branch麯綫和連續性。

Springer-Verlag從1920年開始發行這一個係列教材，最初旨在滿足較高端數學的學習者的需求，陸續增加瞭一些最新的數學進展情況。這個係列現在包括超過400種書，好多已經成為數學中的經典或者已經是該領域的標準參考書。Springer將其中的一些經典重新以平裝的形式發行，使得更多年輕一代學生和研究人員能夠受益。

讀者對象：數學專業的高年級本科生、研究生、教師以及這方麵的專傢學者。

Chapter I.Theory and Reduction of Singularities 1.Algebraic varieties and birational transformations 2.Singularities of plane algebraic curves 3.Singularities of space algebraic curves 4.Topological classification of singularities 5.Singularities of algebraic surfaces 6.The reduction of singularities of an algebraic surfaceChapter II.Linear Systems of Curves t.Definitions and general properties 2.On the conditions imposed by infinitely near base points 3.Complete linear systems 4.Addition and subtraction of linear systems 5.The virtual characters of an arbitrary linear system 6.Exceptional curves 7.Invariance of the virtual characters 8.Virtual characteristic series.Virtual curvesAppendix to Chapter II by JOSEPH LIPMANChapter III.Adjoint Systems and the Theory of Invariants 1.Complete linear systems of plane curves 2.Complete linear systems of surfaces in Sa 3.Subadjoint surfaces 4.Subadjoint systems of a given linear system 5.The distributive property of subadjunction 6.Adjoint systems 7.The residue theorem in its projective form 8.The canonical system 9.The pluricanonical systemsAppendix to Chapter III by DAVID MUMFORDChapter IV.The Arithmetic Genus and the Generalized Theorem of RIEMANN-ROCH 1.The arithmetic genus Pa 2.The theorem of RIEMANN-ROCH on algebraic surfaces 3.The deficiency of the characteristic series of a complete linear system 4.The elimination of exceptional curves and the characterization of ruled surfacesAppendix to Chapter IV by DAVID MUMFORDChapter V.Continuous Non-linear Systems 1.Definitions and general properties 2.Complete continuous systems and algebraic equivalence 3.The completeness of the characteristic series of a complete continuous system 4.The variety of PICARD 5.Equivalence criteria 6.The theory of the base and the number of PICARD 7.The division group and the invariant a of SEVERI 8.On the moduli of algebraic surfacesAppendix to Chapter V by DAVID MUMFORDChapter VI.Topological Properties of Algebraic Surfaces 1.Terminology and notations 2.An algebraic surface as a manifold M4 3.Algebraic cycles on F and their intersections 4.The representation of F upon a multiple plane 5.The deformation of a variable plane section of F 6.The vanishing cycles δi and the invariant cycles 7.The fundamental homologies for the i-cycles on F 8.The reduction of F to a cell 9.The three-dimensional cycles 10.The two-dimensional cycles 11.The group of torsion 12.Homologies between algebraic cycles and algebraic equivalence.The invariant 0 13.The topological theory of algebraic correspondences Appendix to Chapter VI by DAVID MUMFORDChapter VII.Simple and Double Integrals on an Algebraic Surface 1.Classification of integrals 2.Simple integrals of the second kind 3.On the number of independent simple integrals of the first and of the second kind attached to a surface of irregularity q.The fundamental theorem 4.The normal functions of POINCARIE 5.The existence theorem of LEFSCHETZ-PoINCARE 6.Reducible integrals.Theorem of POINCARE 7.Miscellaneous applications of the existence theorem 8.Double integrals of the first kind.Theorem of HODGE 9.Residues of double integrals and the reduction of the double integrals of the second kind 10.Normal double integrals and the determination of the number of independent double integrals of the second kindAppendix to Chapter VII by DAVID MUMFORDChapter VIII.Branch Curves of Multiple Planes and Continuous Systems of Plane Algebraic Curves 1.The problem of existence of algebraic functions of two variables 2.Properties of the fundamental group G 3.The irregularity of cyclic multiple planes 4.Complete continuous systems of plane curves with d nodes 5.Continuous systems of plane algebraic curves with nodes and cuspsAppendix 1 to Chapter VIII by SHREERAM SHANKAR ABHYANKARAppendix 2 to Chapter VIII by DAVID MUMFORDAppendix A.Series of Equivalence 1.Equivalence between sets of points 2.Series of equivalence 3.Invariant series of equivalence 4.Topological and transcendental properties of series of equivalence 5.(Added in 2nd edition, by D.MUMFORD)Appendix B.Correspondences between Algebraic Varieties 1.The fixed point formula of LEFSCHETZ 2.The transcendental equations and the rank of a correspondence 3.The case of two coincident varieties.Correspondences with valence 4.The principle of correspondence of ZEUTHEN-SEVERIBibliographySupplementary Bibliography for Second EditionIndex
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