TAILIEUCHUNG - ALGEBRAIC GEOMETRY

Note immediately one difference between linear equations and polynomial equations: theorems for linear equations don’t depend on which field k you are working over, 1 but those for polynomial equations depend on whether or not k is algebraically closed and (to a lesser extent) whether k has characteristic zero. Since I intend to emphasize the geometry in this course, we will work over algebraically closed fields for the major part of the course. | ALGEBRAIC GEOMETRY . MILNE Abstract. These are the notes for Math 631 taught at the University of Michigan Fall 1993. They are available at jmilne Please send comments and corrections to me at jmilne@. August 24 1996 . First version on the web. June 13 1998 . Added 5 sections 25 pages and an index. Minor changes to Sections 0-8. Contents Introduction 2 0. Algorithms for Polynomials 4 1. Algebraic Sets 14 2. Affine Algebraic Varieties 30 3. Algebraic Varieties 44 4. Local Study Tnngent Plnnes Tnngent Cones Sinuularities 59 5. Projective Varieties and Complete Varieties 80 6. Finite Maps 101 7. Dimension Theory 105 8. Regular Maps and Their Fibres. 117 5. Algebraic Geometry over an Arbitrary Field 131 10. Divisors and Intersection Theory 137 11. Coherent Sheaves Invertible Sheaves. 143 12. Differentials 145 13. Algebraic Varieties over the Complex Numbers 151 14. Further Reading 153 Index 156 @1996 1998 . Milne. You may make one copy of these notes for your own personal use. 1 2 . MILNE Introduction Just as the starting point of linear algebra is the study of the solutions of systems of linear equations n aij Xj di i 1 m j 1 the starting point for algebraic geometry is the study of the solutions of systems of polynomial equations fi Xi Xn 0 i 1 . m fi E k Xi . Xn . Note immediately one difference between linear equations and polynomial equations theorems for linear equations don t depend on which field k you are working over 1 but those for polynomial equations depend on whether or not k is algebraically closed and to a lesser extent whether k has characteristic zero. Since I intend to emphasize the geometry in this course we will work over algebraically closed fields for the major part of the course. A better description of algebraic geometry is that it is the study of polynomial functions and the spaces on which they are defined algebraic varieties just as topology is the study of continuous functions and the .

• Toán học
• Algorithms for Polynomials
• Algebraic Sets
• Algebraic Varieties
• Projective Varieties
• Complete Varieties
• Dimension Theory
• Q classical orthogonal polynomials
• Askey–Wilson polynomials
• Q difference equations
• Fourier coefficients
• Recurrence relations
• Connection problem
• Advanced Algorithms Analysis and Design
• Lecture Advanced Algorithms Analysis and Design
• Bài giảng Phân tích và thiết kế thuật toán nâng cao
• Fast fourier transform
• Coefficient representation
• Discrete fourier transform
• Reduced interval techniques
• Branch and bound method
• Quadratic bounding functions
• Ill conditionned polynomials
• Linear underestimator
• Dual Petrov–Galerkin method
• Generalized Jacobi polynomials
• Nonhomogeneous Dirichlet conditions
• Convergence analysis
• Point boundary value problems based
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