You would hardly find any place where algebraic geometry is not implied. So, this [course_title] will help you understand what Algebraic Geometry really is with easy examples focusing on their varieties, diverse fields, relationships and the language of schemes and properties of morphisms.
By completing this [course_title], you would be able to apply it in statistics, various theories related to Algebraic Geometry, robotics, phylogenetics and so on.
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
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Course Credit: MIT
|Course Introduction, Zariski Topology||00:15:00|
|Projective Varieties, Noether Normalization||00:15:00|
|Grassmannians, Finite and Affine Morphisms||00:20:00|
|More on Finite Morphisms and Irreducible Varieties||00:15:00|
|Function Field, Dominant Maps||00:15:00|
|Product of Varieties, Separatedness||00:15:00|
|Product Topology, Complete Varieties||00:15:00|
|Chow’s Lemma, Blowups||00:15:00|
|Sheaves, Invertible Sheaves on P1||00:15:00|
|Sheaf Functors and Quasi-coherent Sheaves||00:20:00|
|Quasi-coherent and Coherent Sheaves||00:15:00|
|(Quasi)coherent Sheaves on Projective Spaces||00:15:00|
|Divisors and the Picard Group||00:15:00|
|Abel-Jacobi Map, Elliptic Curves||00:15:00|
|Smoothness, Canonical Bundles, the Adjunction Formula||00:10:00|
|(Co)tangent Bundles of Grassmannians||00:05:00|
|Riemann-Hurwitz Formula, Chevalley’s Theorem||00:15:00|
|Bertini’s Theorem, Coherent Sheves on Curves||00:15:00|
|Derived Functors, Existence of Sheaf Cohomology||00:20:00|
|Birkhoff–Grothendieck, Riemann-Roch, Serre Duality||00:10:00|
|Proof of Serre Duality||00:10:00|
|Submit Your Assignment||00:00:00|
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