| Instructor/Recitation | Office | Office hour | |
| Chi Li | HLL-513 |
Tuesday/Wednesday 9:30 am-11 am zoom ID: |
chi.li@rutgers.edu |
| Schedule | Canvas | Rutgers Zoom | Policies | Services |
| Reference: |
Shafarevich: Basic Algebraic Geometry Griffith-Harris: Principles of Algebraic Geometry Fulton: Algebraic Curves |
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Week |
Sections |
Notes |
Homeworks |
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Week 1: 9/1-9/5 |
1.1: Plane curves 1.2: Rational curves |
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Week 2: 9/8-9/12 |
1.4: Singular and non-singular points 1.5: Projective plane |
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Week 3: 9/15-9/19 |
Bezout theorem Noether's theorem: statement |
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Week 4: 9/22-9/26 |
2.1: Closed subsets of affine space 2.2-2.3: Regular functions, regular maps 3.1: Irreducible algebraic subsets |
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Week 5: 9/30 -10/3 |
3.2-3.3: Rational functions, rational maps 4.1: Closed subsets of projective space 4.2-4.3: Regular functions, rational functions |
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Week 6: 10/6-10/10 |
Proof of Noether's theorem
5.1-5.2: Products, Images |
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Week 7: 10/13-10/17 |
5.3-5.4: finite maps, Noether normalization 6.1: Dimension 6.3: Dimension of fibres |
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Week 8: 10/20-10/24 |
Complex manifolds Sheaves and cohomology |
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Week 9: 10/27-10/31 |
Dolbeault theorem Hodge theorem |
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Week 10: 11/3-11/7 |
Divisors and line bundles Vector bundles |
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Week 11: 11/10 -11/14 |
Riemann-Roch formula for curves Linear systems on curves |
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Week 12: 11/17 -11/21 |
Canonical curves Special linear systems |
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Week 13: 11/24-11/28 |
Hyperelliptic curves Jacobian of curves Abel's theorem |
Thanksgiving 11/23-11/26 | |
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Week 14: 12/1-12/5 |
Blow ups and birational transformations Cremona transformations |
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Week 15: 12/8-12/12 |
Grassmannians |
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Week 16: 12/15-12/22 |
Final Exam |
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• Lectures: Regular attendance and participation are expected and are integral to your success in this class.
• Quizzes: No makeups. The lowest(or missing) score will be dropped.
• Exams: If you must miss an exam, you must notify your professor as soon as possible. A makeup can be offered only if the absence is due to an unavoidable emergency or religious observance.
All students in the course are expected to be familiar with and abide by the academic integrity policy. Violations of the policy are taken very seriously.
The Office of Disability Services (ODS) determines full disability policies and procedures. Students with disabilities requesting accommodations must do the following: (1) consult ODS policies on requesting accommodations, and (2) present a Letter of Accommodations to the course coordinator and their instructor as early in the term as possible (see https://ods.rutgers.edu/letter-accommodation )
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