1、世界图书出版公司获得Springer-Verlag授权，新近独家重印出版以下数学类图书：1.Mathematics in Medicine the Life Sciences(TAM Vol.10)2.Differential Equations Their Applications 4th ed.(TAM Vol.11)3Introduction to Numerical Analysis 2nd ed.(TAM Vol.12).Growth Diffusion Phenomena:Mathematical Frameworks Applications(TAM VoL.14)5The Ma
2、thematical Theory of Finite Element Methods(TAM Vol.15)Introductions to Mechanics Symmetry(TAM Vol.17)7.Coding Information Theory(GTM Vol.134)8Advanced Linear Algebra(GTM Vol.135)A Course in Computational Algebraic Number Theory(GTM Vol.138)10.Real Functional Analysis 3rd ed.(GTM Vol.142)11.Computab
3、ility(GTM Vol.146)12.Algebraic Topology:A First Course(GTM Vol.153)13.Differential Riemannian Manifolds(GTM Vol.160)14.Basic Algebraic Geometry 1:Varieties in Projective Space 2nd ed.15.Basic Algebraic Geometry 2:Schemes Complex Manifolds 2nd ed.16.Stochastic Differential Equations 4th ed.(Universit
4、ext)17.Numerical Approximation of Partial Differential Equations(SSCM Vol.23)18Understanding Nonlinear Dynamics1SBN7-5062-3620-69787506236201WB3620定价：43.00元Preface to Books 2 and 3Books 2 and 3 correspond to Chap.V-IX of the first edition.They studyschemes and complex manifolds,two notions that gene
5、ralise in different di-rections the varieties in projective space studied in Book 1.Introducing themleads also to new results in the theory of projective varieties.For example,itis within the framework of the theory of schemes and abstract varieties thatwe find the natural proof of the adjunction fo
6、rmula for the genus of a curve,which we have already stated and applied in Chap.IV,2.3.The theory ofcomplex analytic manifolds leads to the study of the topology of projectivevarieties over the field of complex numbers.For some questions it is onlyhere that the natural and historical logic of the su
7、bject can be reasserted;for example,differential forms were constructed in order to be integrated,aprocess which only makes sense for varieties over the(real or)complex fields.Changes from the First EditionAs in the Book 1,there are a number of additions to the text,of which thefollowing two are the
8、 most important.The first of these is a discussion of thenotion of the algebraic variety classifying algebraic or geometric objects ofsome type.As an example we work out the theory of the Hilbert polynomialand the Hilbert scheme.I am very grateful to V.I.Danilov for a series ofrecommendations on thi
9、s subject.In particular the proof of Chap.VI,4.3,Theorem 3 is due to him.The second addition is the definition and basicproperties of a Kahler metric,and a description(without proof)of Hodgestheorem.PrerequisitesVarieties in projective space will provide us with the main supply of example8,and the t
10、heoretical apparatus of Book 1 will be used,but by no means all ofit.Different sections use different parts,and there is no point in giving exactindications.References to the Appendix are to the Algebraic Appendix atthe end of Book 1.Prerequisites for the reader of Books 2 and 3 are as follows:for.Book 2,the same as for Book 1;for Book 3,the definition of differentiable manifold,
