Modules / Lectures

Sl.No Chapter Name English
1What is Algebraic Geometry?PDF unavailable
2The Zariski Topology and Affine SpacePDF unavailable
3Going back and forth between subsets and idealsPDF unavailable
4Irreducibility in the Zariski TopologyPDF unavailable
5Irreducible Closed Subsets Correspond to Ideals Whose Radicals are PrimePDF unavailable
6Understanding the Zariski Topology on the Affine Line; The Noetherian property in Topology and in AlgebraPDF unavailable
7Basic Algebraic Geometry : Varieties, Morphisms, Local Rings, Function Fields and NonsingularityPDF unavailable
8Topological Dimension, Krull Dimension and Heights of Prime IdealsPDF unavailable
9The Ring of Polynomial Functions on an Affine VarietyPDF unavailable
10Geometric Hypersurfaces are Precisely Algebraic HypersurfacesPDF unavailable
11Why Should We Study Affine Coordinate Rings of Functions on Affine Varieties ?PDF unavailable
12Capturing an Affine Variety Topologically From the Maximal Spectrum of its Ring of FunctionsPDF unavailable
13Analyzing Open Sets and Basic Open Sets for the Zariski TopologyPDF unavailable
14The Ring of Functions on a Basic Open Set in the Zariski TopologyPDF unavailable
15Quasi-Compactness in the Zariski Topology; Regularity of a Function at a point of an Affine VarietyPDF unavailable
16What is a Global Regular Function on a Quasi-Affine Variety?PDF unavailable
17Characterizing Affine Varieties; Defining Morphisms between Affine or Quasi-Affine VarietiesPDF unavailable
18Translating Morphisms into Affines as k-Algebra maps and the Grand Hilbert NullstellensatzPDF unavailable
19Morphisms into an Affine Correspond to k-Algebra Homomorphisms from its Coordinate Ring of FunctionsPDF unavailable
20The Coordinate Ring of an Affine Variety Determines the Affine Variety and is Intrinsic to itPDF unavailable
21Automorphisms of Affine Spaces and of Polynomial Rings - The Jacobian Conjecture; The Punctured Plane is Not AffinePDF unavailable
22The Various Avatars of Projective n-spacePDF unavailable
23Gluing (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 IdealPDF unavailable
24Translating Projective Geometry into Graded Rings and Homogeneous IdealsPDF unavailable
25Expanding the Category of Varieties to Include Projective and Quasi-Projective VarietiesPDF unavailable
26Translating Homogeneous Localisation into Geometry and BackPDF unavailable
27Adding a Variable is Undone by Homogenous Localization - What is the Geometric Significance of this Algebraic Fact ?PDF unavailable
28Doing Calculus Without Limits in Geometry ? PDF unavailable
29The Birth of Local Rings in Geometry and in AlgebraPDF unavailable
30The Formula for the Local Ring at a Point of a Projective Variety Or Playing with Localisations, Quotients, Homogenisation and Dehomogenisation !PDF unavailable
31The Field of Rational Functions or Function Field of a Variety - The Local Ring at the Generic PointPDF unavailable
32Fields of Rational Functions or Function Fields of Affine and Projective Varieties and their Relationships with DimensionsPDF unavailable
33Global Regular Functions on Projective Varieties are Simply the Constants PDF unavailable
34The d-Uple Embedding and the Non-Intrinsic Nature of the Homogeneous Coordinate Ring of a Projective Variety PDF unavailable
35The 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
36The Importance of Local Rings - A Rational Function in Every Local Ring is Globally Regular PDF unavailable
37Geometric Meaning of Isomorphism of Local Rings - Local Rings are Almost GlobalPDF unavailable
38Local Ring Isomorphism,Equals Function Field Isomorphism, Equals Birationality PDF unavailable
39Why Local Rings Provide Calculus Without Limits for Algebraic Geometry Pun Intended!PDF unavailable
40How Local Rings Detect Smoothness or Nonsingularity in Algebraic GeometryPDF unavailable
41Any Variety is a Smooth Manifold with or without Non-Smooth BoundaryPDF unavailable
42Any Variety is a Smooth Hypersurface On an Open Dense SubsetPDF unavailable

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2BengaliNot Available
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