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Tutorial 4: More Applications of Dimension Theory
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Classroom Contents
Introduction to Algebraic Geometry
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- 1 Introduction To Algebraic Geometry - Course Introduction
- 2 Topics in Commutative Algebra - Part 1
- 3 Topics in Commutative Algebra - Part 2
- 4 Topics in Commutative Algebra - Part 3
- 5 Topics in Commutative Algebra - Part 4
- 6 Topics in Commutative Algebra - Part 5
- 7 Tutorial 1: Cayley-Hamilton Theorem, Nakayama's Lemma
- 8 Topics in Commutative Algebra: Part 6
- 9 Topics in Commutative Algebra: Part 7
- 10 Topics in Commutative Algebra: Part 8
- 11 Affine Algebraic Sets - Part 1
- 12 Affine Algebraic Sets - Part 2
- 13 Tutorial 2: Noether Normalization Lemma,Some Important Results in Dimension Theory
- 14 Regular Morphisms
- 15 Abstract Algebraic Sets
- 16 Zariski Topology on Affine Space
- 17 Irreducible Affine Algebraic Sets
- 18 Ring of Regular Functions
- 19 Projective Space
- 20 Tutorial 3: Some Applications of Dimension Theory
- 21 Zariski Topology on Projective Space
- 22 Affine Open Cover of Projective Space
- 23 Projective & Quasi-Projective Varieties
- 24 Regular Functions on Quasi-Projective Varieties
- 25 Presheaves & Sheaves
- 26 Morphism of Presheaves/Sheaves
- 27 Tutorial 4: More Applications of Dimension Theory
- 28 A Brief Overview of Sheaf Theory - Part 1
- 29 A Brief Overview of Sheaf Theory - Part 2
- 30 A Brief Overview of Sheaf Theory - Part 3
- 31 Prevarieties
- 32 Sheaf of Regular Functions
- 33 Ring of Germs of Regular Functions at a point, Field of Rational Functions
- 34 Tutorial 5: Sheafification
- 35 Ring of Regular Functions, Local Ring at a Point,and Field of Rational Functions of an AffineVariety
- 36 Equivalence of Categories of the Category of Affine Varieties over a Field k and the Category
- 37 Equivalence of Categories of the Category of Affine Varieties over a Field k (Contd.)
- 38 Some Examples, Open Immersions & Closed Immersions
- 39 Product of Quasi-affine Varieties
- 40 Diagonal Morphisms, Abstract Varieties
- 41 Tutorial 6: Normal Varieties & Normalization of a Variety
- 42 Projective Varieties Revisited: Part 1
- 43 Projective Varieties Revisited: Part 2
- 44 Global Regular Functions on ProjectiveVarieties are Constants : Part 1
- 45 Global Regular Functions on ProjectiveVarieties are Constants : Part 2
- 46 Product of Prevarieties : Part 1
- 47 Product of Prevarieties : Part 2
- 48 Tutorial 7 : A Result on Tensor Products of k-algebras
- 49 Morphisms of Prevarieties : Part 1
- 50 Morphisms of Prevarieties : Part 2
- 51 Finite Morphisms : Part 1
- 52 Finite Morphisms : Part 2
- 53 Fiber Products
- 54 Tutorial 8 : Finite Morphisms
- 55 Immersions
- 56 Fiber Products, Separatedness
- 57 Criterion of Separatedness
- 58 Proper Morphisms & Complete Varieties
- 59 Tutorial 9 : Closed Immersions & Graph of a Morphism
- 60 Projective Varieties are Complete
- 61 Zariski Tangent Space, Singular & Nonsingular Points
- 62 Smooth Points Form a Non-empty Open Subset
- 63 Blow-Ups, Rational Maps & Birational Maps
- 64 Tutorial 10 : Zariski Tangent Space at a Point of an Affine Variety
- 65 Blow-Ups ( Contd.)
- 66 Smooth Morphisms
- 67 Bertini's Theorem
- 68 Sard's Theorem
- 69 Tutorial 11 : Dimension of fiber of a morphism
- 70 Introduction to Affine Schemes : Spectrum of a Ring
- 71 Introduction to Affine Schemes : Topology on Spec A
- 72 Introduction to Affine Schemes : Topology on Spec A ( Contd. )
- 73 Introduction to Affine Schemes : Sheaf Structure on Spec A
- 74 Abstract Non-singular Curves : Part 1
- 75 Abstract Non-singular Curves : Part 2
- 76 Tutorial 12 : Extension of Regular Functions
