| Preface Acknowledgments Using This Book PART I: EXAMPLES OF VARIETIES AND MAPS LECTURE 1 Affine and Projective Varieties LECTURE 2 Regular Functions and Maps LECTURE 3 Cones, Projections, and More About Products LECTURE 4 Families and Parameter Spaces LECTURE 5 Ideals of Varieties, Irreducible Decomposition, and the Nullstellensatz LECTURE 6 Grassmannians and Related Varieties LECTURE 7 Rational Functions and Rational Maps LECTURE 8 More Examples LECTURE 9 Determinantal Varieties LECTURE 10 Algebraic Groups PART II: ATTRIBUTES OF VARIETIES LECTURE 11 Definitions of Dimension and Elementary Examples LECTURE 12 More Dimension Computations LECTURE 13 Hilbert Polynomials LECTURE 14 Smoothness and Tangent Spaces LECTURE 15 Gauss Maps, Tangential and Dual Varieties LECTURE 16 Tangent Spaces to Grassmannians LECTURE 17 Further Topics Involving Smoothness and Tangent Spaces LECTURE 18 Degree LECTURE 19 Further Examples and Applications of Degree LECTURE 20 Singular Points and Tangent Cones LECTURE 21 Parameter Spaces and Moduli Spaces LECTURE 22 QuadricsHints for Selected Exercises References Index |
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