最 低 价：￥524.70
定 价：￥583.00
作 者：DavidEisenbud，Daniel R. Grayson 等著 著
出 版 社：湖南文艺出版社
出版时间：2001-10-1
I S B N：9783540422303
| Preface List of Contributors Part I Introducing Macaulay 2 Ideals, Varieties and Macaulay 2 Bernd Sturmfels 1 A Curve in Affine Three-Space 2 Intersecting Our Curve With a Surface 3 Changing the Ambient Polynomial Ring 4 Monomials Under the Staircase 5 Pennies, Nickels, Dimes and Quarters References Projective Geometry and Homological Algebra David Eisenbud 1 The Twisted Cubic 2 The Cotangent Bundle of I?3 3 The Cotangent Bundle of a Projective Variety 4 Intersections by Serre's Method 5 A Mystery Variety in ]?3 Appendix A. How the "Mystery Variety" was Made References Data Types, Fhlnctions, and Programming Daniel R. Grayson and Michael E. Stillman 1 Basic Data Types 2 Control Structures 3 Input and Output 4 Hash Tables 5 Methods 6 Pointers to the Source Code References Teaching the Geometry of Schemes Gregory G. Smith and Bernd Sturmfels 1 Distinguished Open Sets 2 Irreducibility 3 Singular Point 4 Fields of Definition 5 Multiplicity 6 Flat Families 7 Bezout's Theorem 8 Constructing Blow-ups 9 A Classic Blow-up 10 Fano Schemes References Part II Mathematical Computations Monomial Ideals Serkan Hosaten and Gregory G. Smith 1 The Basics of Monomial Ideals 2 Primary Decomposition 3 Standard Pairs 4 Generic Initial Ideals 5 The Chain Property References From Enumerative Geometry to Solving Systems of Polynomial Equations Frank Sottile 1 Introduction 2 Solving Systems of Polynomials 3 Some Enumerative Geometry 4 Schubert Calculus 5 The 12 Lines: Reprise References Resolutions and Cohomology over Complete Intersections Luchezar L. Avramov and Daniel R. Grayson 1 Matrix Factorizations 2 Graded Algebras 3 UniversM Homotopies 4 Cohomology Operators 5 Computation of Ext Modules 6 Invariants of Modules 7 Invariants of Pairs of Modules Appendix A. Gradings References Algorithms for the Toric Hilbert Scheme Sheaf Algorithms Using the Exterior Algebra Needles in a Haystack:Special Varieties via Small Fields D-modules and Cohomology of Varieties Index |
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