# Introduction To Algebraic Geometry

- Institution: IIT Madras
- Department: Mathematics
- Teacher: Prof. Arijit Dey
- Level: Graduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106168)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106168)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

Commutative algebra and Algebraic geometry are twin topics. They are very much interrelated. Giving a course in algebraic geometry requires good grasp of commutative algebra.. This course will motivate students to learn more advanced topics in commutative algebra and algebraic geometry. I am hoping person who are interested to learn commutative algebra and algebraic geometry will see a beautiful mixture of these two important topics in this course.

Prerequisites: Knowledge in basic algebra (groups/rings/fields/modules). Litttle knowledge in commutative algebra for e.g. prime and maximal ideals of a ring, tensor product of modules, localisation. A little knowledge in general topology is also required.

## Lectures

1. [Topics in Commutative Algebra - Part 1](https://invisiblenetwork.ai/learn/nptel/111106168/dd967199669d) (YouTube)
2. [Topics in Commutative Algebra - Part 2](https://invisiblenetwork.ai/learn/nptel/111106168/924b27f884e9) (YouTube)
3. [Topics in Commutative Algebra - Part 3](https://invisiblenetwork.ai/learn/nptel/111106168/b22ac1278e5d) (YouTube)
4. [Topics in Commutative Algebra - Part 4](https://invisiblenetwork.ai/learn/nptel/111106168/81ecf8e0f092) (YouTube)
5. [Topics in Commutative Algebra - Part 5](https://invisiblenetwork.ai/learn/nptel/111106168/cd60ac648a66) (YouTube)
6. [Tutorial 1: Cayley-Hamilton Theorem, Nakayama's Lemma](https://invisiblenetwork.ai/learn/nptel/111106168/bb349a18545e) (YouTube)
7. [Topics in Commutative Algebra: Part 6](https://invisiblenetwork.ai/learn/nptel/111106168/5ef552d1a97b) (YouTube)
8. [Topics in Commutative Algebra: Part 7](https://invisiblenetwork.ai/learn/nptel/111106168/004e80e9fac5) (YouTube)
9. [Topics in Commutative Algebra: Part 8](https://invisiblenetwork.ai/learn/nptel/111106168/73c99b1b4824) (YouTube)
10. [Affine Algebraic Sets - Part 1](https://invisiblenetwork.ai/learn/nptel/111106168/0611bf4b2ef8) (YouTube)
11. [Affine Algebraic Sets - Part 2](https://invisiblenetwork.ai/learn/nptel/111106168/db45f964af5f) (YouTube)
12. [Tutorial 2: Noether Normalization Lemma, Some Important Results in Dimension Theory](https://invisiblenetwork.ai/learn/nptel/111106168/ec7c92bb36be) (YouTube)
13. [Regular Morphisms](https://invisiblenetwork.ai/learn/nptel/111106168/d45175604e68) (YouTube)
14. [Abstract Algebraic Sets](https://invisiblenetwork.ai/learn/nptel/111106168/47b2694b2428) (YouTube)
15. [Zariski Topology on Affine Space](https://invisiblenetwork.ai/learn/nptel/111106168/401b8a6aef02) (YouTube)
16. [Irreducible Affine Algebraic Sets](https://invisiblenetwork.ai/learn/nptel/111106168/c52fa2efd37a) (YouTube)
17. [Ring of Regular Functions](https://invisiblenetwork.ai/learn/nptel/111106168/62c7f94250b6) (YouTube)
18. [Projective Space](https://invisiblenetwork.ai/learn/nptel/111106168/25e9abae0cfe) (YouTube)
19. [Tutorial 3: Some Applications of Dimension Theory](https://invisiblenetwork.ai/learn/nptel/111106168/54b8f291ee10) (YouTube)
20. [Zariski Topology on Projective Space](https://invisiblenetwork.ai/learn/nptel/111106168/dcd1c6ee100a) (YouTube)
21. [Affine Open Cover of Projective Space](https://invisiblenetwork.ai/learn/nptel/111106168/de29812e3000) (YouTube)
22. [Projective & Quasi-Projective Varieties](https://invisiblenetwork.ai/learn/nptel/111106168/01ef5c531b60) (YouTube)
23. [Regular Functions on Quasi-Projective Varieties](https://invisiblenetwork.ai/learn/nptel/111106168/387484e6ead6) (YouTube)
24. [Presheaves & Sheaves](https://invisiblenetwork.ai/learn/nptel/111106168/ac85d4c7d578) (YouTube)
25. [Morphism of Presheaves/Sheaves](https://invisiblenetwork.ai/learn/nptel/111106168/c774848cd640) (YouTube)
26. [Tutorial 4: More Applications of Dimension Theory](https://invisiblenetwork.ai/learn/nptel/111106168/d6f610a097d7) (YouTube)
27. [A Brief Overview of Sheaf Theory - Part 1](https://invisiblenetwork.ai/learn/nptel/111106168/51145096a2f9) (YouTube)
28. [A Brief Overview of Sheaf Theory - Part 2](https://invisiblenetwork.ai/learn/nptel/111106168/0210ed456a25) (YouTube)
29. [A Brief Overview of Sheaf Theory - Part 3](https://invisiblenetwork.ai/learn/nptel/111106168/dfdeb4c04244) (YouTube)
30. [Prevarieties](https://invisiblenetwork.ai/learn/nptel/111106168/90760c95af2d) (YouTube)
31. [Sheaf of Regular Functions](https://invisiblenetwork.ai/learn/nptel/111106168/2a828a82be37) (YouTube)
32. [Ring of Germs of Regular Functions at a point, Field of Rational Functions](https://invisiblenetwork.ai/learn/nptel/111106168/86873b439d5c) (YouTube)
33. [Tutorial 5: Sheafification](https://invisiblenetwork.ai/learn/nptel/111106168/f61a39d22bde) (YouTube)
34. [Ring of Regular Functions, Local Ring at a Point, and Field of Rational Functions of an Affine Variety](https://invisiblenetwork.ai/learn/nptel/111106168/6b3155f2bf8b) (YouTube)
35. [Equivalence of Categories of the Category of Affine Varieties over a Field k and the Category of Finitely Generated Integral Domains over k](https://invisiblenetwork.ai/learn/nptel/111106168/1c6ccb5d27ce) (YouTube)
36. [Equivalence of Categories of the Category of Affine Varieties over a Field k and the Category of Finitely Generated Integral Domains over k (Contd.)](https://invisiblenetwork.ai/learn/nptel/111106168/fcdabcb290aa) (YouTube)
37. [Some Examples, Open Immersions & Closed Immersions](https://invisiblenetwork.ai/learn/nptel/111106168/ba19b2a19c18) (YouTube)
38. [Product of Quasi-affine Varieties](https://invisiblenetwork.ai/learn/nptel/111106168/4cb0e0cd746c) (YouTube)
39. [Diagonal Morphisms, Abstract Varieties](https://invisiblenetwork.ai/learn/nptel/111106168/6272d6cfb765) (YouTube)
40. [Tutorial 6: Normal Varieties & Normalization of a Variety](https://invisiblenetwork.ai/learn/nptel/111106168/bdba7a4c3e37) (YouTube)
41. [Projective Varieties Revisited: Part 1](https://invisiblenetwork.ai/learn/nptel/111106168/5bbe87a9a985) (YouTube)
42. [Projective Varieties Revisited: Part 2](https://invisiblenetwork.ai/learn/nptel/111106168/874187885048) (YouTube)
43. [Global Regular Functions on Projective Varieties are Constants : Part 1](https://invisiblenetwork.ai/learn/nptel/111106168/f78ef47d8d42) (YouTube)
44. [Global Regular Functions on Projective Varieties are Constants : Part 2](https://invisiblenetwork.ai/learn/nptel/111106168/a8a14c32ee40) (YouTube)
45. [Product of Prevarieties : Part 1](https://invisiblenetwork.ai/learn/nptel/111106168/4ae8e45b5dcd) (YouTube)
46. [Product of Prevarieties : Part 2](https://invisiblenetwork.ai/learn/nptel/111106168/d34d2325d5a7) (YouTube)
47. [Tutorial 7 : A Result on Tensor Products of k-algebras](https://invisiblenetwork.ai/learn/nptel/111106168/29db6b8e7c47) (YouTube)
48. [Morphisms of Prevarieties : Part 1](https://invisiblenetwork.ai/learn/nptel/111106168/9f9fec0fec0f) (YouTube)
49. [Morphisms of Prevarieties : Part 2](https://invisiblenetwork.ai/learn/nptel/111106168/0002bb1d3740) (YouTube)
50. [Finite Morphisms : Part 1](https://invisiblenetwork.ai/learn/nptel/111106168/29d4d3f4e592) (YouTube)
51. [Finite Morphisms : Part 2](https://invisiblenetwork.ai/learn/nptel/111106168/75046aef51b8) (YouTube)
52. [Fiber Products](https://invisiblenetwork.ai/learn/nptel/111106168/8a2d3732e4f6) (YouTube)
53. [Tutorial 8 : Finite Morphisms](https://invisiblenetwork.ai/learn/nptel/111106168/765ad827f40f) (YouTube)
54. [Immersions](https://invisiblenetwork.ai/learn/nptel/111106168/c88867fa37be) (YouTube)
55. [Fiber Products, Separatedness](https://invisiblenetwork.ai/learn/nptel/111106168/79f291f2dace) (YouTube)
56. [Criterion of Separatedness](https://invisiblenetwork.ai/learn/nptel/111106168/1bf16717f192) (YouTube)
57. [Proper Morphisms & Complete Varieties](https://invisiblenetwork.ai/learn/nptel/111106168/e47cf14caffb) (YouTube)
58. [Tutorial 9 : Closed Immersions & Graph of a Morphism](https://invisiblenetwork.ai/learn/nptel/111106168/af5024a84b38) (YouTube)
59. [Projective Varieties are Complete](https://invisiblenetwork.ai/learn/nptel/111106168/4e5d0c6ddb1c) (YouTube)
60. [Zariski Tangent Space, Singular & Nonsingular Points](https://invisiblenetwork.ai/learn/nptel/111106168/46d8c34c6e1c) (YouTube)
61. [Smooth Points Form a Non-empty Open Subset](https://invisiblenetwork.ai/learn/nptel/111106168/a7af80be11d3) (YouTube)
62. [Blow-Ups, Rational Maps & Birational Maps](https://invisiblenetwork.ai/learn/nptel/111106168/be2afe0bee28) (YouTube)
63. [Tutorial 10 : Zariski Tangent Space at a Point of an Affine Variety](https://invisiblenetwork.ai/learn/nptel/111106168/2dd80c7ff372) (YouTube)
64. [Blow-Ups ( Contd.)](https://invisiblenetwork.ai/learn/nptel/111106168/ce832ef59c00) (YouTube)
65. [Smooth Morphisms](https://invisiblenetwork.ai/learn/nptel/111106168/63a6381dde0d) (YouTube)
66. [Bertini's Theorem](https://invisiblenetwork.ai/learn/nptel/111106168/3363f03dec7e) (YouTube)
67. [Sard's Theorem](https://invisiblenetwork.ai/learn/nptel/111106168/3df5a6462827) (YouTube)
68. [Tutorial 11 : Dimension of fiber of a morphism](https://invisiblenetwork.ai/learn/nptel/111106168/c80ed01bd9fa) (YouTube)
69. [Introduction to Affine Schemes : Spectrum of a Ring](https://invisiblenetwork.ai/learn/nptel/111106168/f8ab1f27eb1b) (YouTube)
70. [Introduction to Affine Schemes : Topology on Spec A](https://invisiblenetwork.ai/learn/nptel/111106168/c8df469fac64) (YouTube)
71. [Introduction to Affine Schemes : Topology on Spec A ( Contd. )](https://invisiblenetwork.ai/learn/nptel/111106168/6314d25092ad) (YouTube)
72. [Introduction to Affine Schemes : Sheaf Structure on Spec A](https://invisiblenetwork.ai/learn/nptel/111106168/aa96aa5d80b5) (YouTube)
73. [Abstract Non-singular Curves : Part 1](https://invisiblenetwork.ai/learn/nptel/111106168/05087a952b03) (YouTube)
74. [Abstract Non-singular Curves : Part 2](https://invisiblenetwork.ai/learn/nptel/111106168/b118605544d0) (YouTube)
75. [Tutorial 12 : Extension of Regular Functions](https://invisiblenetwork.ai/learn/nptel/111106168/73fc75d1a075) (YouTube)