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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.

### Assessment

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.

### Certification

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

Having an Official Edukite Certification is a great way to celebrate and share your success. You can:

• Show it to prove your success

Course Credit: MIT

### Course Curriculum

 Module: 01 Course Introduction, Zariski Topology 00:15:00 Affine Varieties 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 Module: 02 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 Module: 03 Sheaf Functors and Quasi-coherent Sheaves 00:20:00 Quasi-coherent and Coherent Sheaves 00:15:00 Invertible Sheaves 00:10:00 (Quasi)coherent Sheaves on Projective Spaces 00:15:00 Divisors and the Picard Group 00:15:00 Module: 04 Bezout’s Theorem 00:15:00 Abel-Jacobi Map, Elliptic Curves 00:15:00 Kähler Differentials 00:15:00 Smoothness, Canonical Bundles, the Adjunction Formula 00:10:00 (Co)tangent Bundles of Grassmannians 00:05:00 Module: 05 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 Assessment Submit Your Assignment 00:00:00 Certification 00:00:00

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