Modules / Lectures

Sl.No | Chapter Name | English |
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1 | What is Algebraic Geometry? | PDF unavailable |

2 | The Zariski Topology and Affine Space | PDF unavailable |

3 | Going back and forth between subsets and ideals | PDF unavailable |

4 | Irreducibility in the Zariski Topology | PDF unavailable |

5 | Irreducible Closed Subsets Correspond to Ideals Whose Radicals are Prime | PDF unavailable |

6 | Understanding the Zariski Topology on the Affine Line; The Noetherian property in Topology and in Algebra | PDF unavailable |

7 | Basic Algebraic Geometry : Varieties, Morphisms, Local Rings, Function Fields and Nonsingularity | PDF unavailable |

8 | Topological Dimension, Krull Dimension and Heights of Prime Ideals | PDF unavailable |

9 | The Ring of Polynomial Functions on an Affine Variety | PDF unavailable |

10 | Geometric Hypersurfaces are Precisely Algebraic Hypersurfaces | PDF unavailable |

11 | Why Should We Study Affine Coordinate Rings of Functions on Affine Varieties ? | PDF unavailable |

12 | Capturing an Affine Variety Topologically From the Maximal Spectrum of its Ring of Functions | PDF unavailable |

13 | Analyzing Open Sets and Basic Open Sets for the Zariski Topology | PDF unavailable |

14 | The Ring of Functions on a Basic Open Set in the Zariski Topology | PDF unavailable |

15 | Quasi-Compactness in the Zariski Topology; Regularity of a Function at a point of an Affine Variety | PDF unavailable |

16 | What is a Global Regular Function on a Quasi-Affine Variety? | PDF unavailable |

17 | Characterizing Affine Varieties; Defining Morphisms between Affine or Quasi-Affine Varieties | PDF unavailable |

18 | Translating Morphisms into Affines as k-Algebra maps and the Grand Hilbert Nullstellensatz | PDF unavailable |

19 | Morphisms into an Affine Correspond to k-Algebra Homomorphisms from its Coordinate Ring of Functions | PDF unavailable |

20 | The Coordinate Ring of an Affine Variety Determines the Affine Variety and is Intrinsic to it | PDF unavailable |

21 | Automorphisms of Affine Spaces and of Polynomial Rings - The Jacobian Conjecture; The Punctured Plane is Not Affine | PDF unavailable |

22 | The Various Avatars of Projective n-space | PDF unavailable |

23 | Gluing (n+1) copies of Affine n-Space to Produce Projective n-space in Topology, Manifold Theory and Algebraic Geometry; The Key to the Definition of a Homogeneous Ideal | PDF unavailable |

24 | Translating Projective Geometry into Graded Rings and Homogeneous Ideals | PDF unavailable |

25 | Expanding the Category of Varieties to Include Projective and Quasi-Projective Varieties | PDF unavailable |

26 | Translating Homogeneous Localisation into Geometry and Back | PDF unavailable |

27 | Adding a Variable is Undone by Homogenous Localization - What is the Geometric Significance of this Algebraic Fact ? | PDF unavailable |

28 | Doing Calculus Without Limits in Geometry ? | PDF unavailable |

29 | The Birth of Local Rings in Geometry and in Algebra | PDF unavailable |

30 | The Formula for the Local Ring at a Point of a Projective Variety Or Playing with Localisations, Quotients, Homogenisation and Dehomogenisation ! | PDF unavailable |

31 | The Field of Rational Functions or Function Field of a Variety - The Local Ring at the Generic Point | PDF unavailable |

32 | Fields of Rational Functions or Function Fields of Affine and Projective Varieties and their Relationships with Dimensions | PDF unavailable |

33 | Global Regular Functions on Projective Varieties are Simply the Constants | PDF unavailable |

34 | The d-Uple Embedding and the Non-Intrinsic Nature of the Homogeneous Coordinate Ring of a Projective Variety | PDF unavailable |

35 | The Importance of Local Rings - A Morphism is an Isomorphism if it is a Homeomorphism and Induces Isomorphisms at the Level of Local Rings | PDF unavailable |

36 | The Importance of Local Rings - A Rational Function in Every Local Ring is Globally Regular | PDF unavailable |

37 | Geometric Meaning of Isomorphism of Local Rings - Local Rings are Almost Global | PDF unavailable |

38 | Local Ring Isomorphism,Equals Function Field Isomorphism, Equals Birationality | PDF unavailable |

39 | Why Local Rings Provide Calculus Without Limits for Algebraic Geometry Pun Intended! | PDF unavailable |

40 | How Local Rings Detect Smoothness or Nonsingularity in Algebraic Geometry | PDF unavailable |

41 | Any Variety is a Smooth Manifold with or without Non-Smooth Boundary | PDF unavailable |

42 | Any Variety is a Smooth Hypersurface On an Open Dense Subset | PDF unavailable |

Sl.No | Language | Book link |
---|---|---|

1 | English | Not Available |

2 | Bengali | Not Available |

3 | Gujarati | Not Available |

4 | Hindi | Not Available |

5 | Kannada | Not Available |

6 | Malayalam | Not Available |

7 | Marathi | Not Available |

8 | Tamil | Not Available |

9 | Telugu | Not Available |