PMATH 764
Introduction to Algebraic Geometry
Winter 2022
Topics
- Affine and projective algebraic sets
- Hilbert’s Nullstellensatz
- Coordinate rings and polynomial maps
- Rational functions and local rings
- Plane curves, tangency and multiplicity
- Intersection numbers and Bézout’s theorem
- Divisor class groups
Undated · Algebraic Geometry
Topics
- Affine Algebraic Varieties
- Ideals in Polynomial Rings
- Points and Irreducible Varieties
- Affine Maps and Affine Equivalence
- Polynomial Maps and Isomorphism
- Rational Maps and Birational Equivalence
- Ring Extensions and Field Extensions
- Hilbert's Nullstellensatz
- Dimension
- Local Dimension and Singularity
- Projective Varieties
Readings
- Chapter 1. Affine Algebraic Varieties — https://www.math.uwaterloo.ca/~snew/PMATH464/chap1.pdf
- Chapter 2. Ideals in Polynomial Rings — https://www.math.uwaterloo.ca/~snew/PMATH464/chap2.pdf
- Chapter 3. Points and Irreducible Varieties — https://www.math.uwaterloo.ca/~snew/PMATH464/chap3.pdf
- Chapter 4. Affine Maps and Affine Equivalence — https://www.math.uwaterloo.ca/~snew/PMATH464/chap4.pdf
- Chapter 5. Polynomial Maps and Isomorphism — https://www.math.uwaterloo.ca/~snew/PMATH464/chap5.pdf
- Chapter 6. Rational Maps and Birational Equivalence — https://www.math.uwaterloo.ca/~snew/PMATH464/chap6.pdf
- Chapter 7. Ring Extensions and Field Extensions — https://www.math.uwaterloo.ca/~snew/PMATH464/chap7.pdf
- Chapter 8. Hilbert's Nullstellensatz — https://www.math.uwaterloo.ca/~snew/PMATH464/chap8.pdf
- Chapter 9. Dimension — https://www.math.uwaterloo.ca/~snew/PMATH464/chap9.pdf
- Chapter 10. Local Dimension and Singularity — https://www.math.uwaterloo.ca/~snew/PMATH464/chap10.pdf
- Chapter 11. Projective Varieties — https://www.math.uwaterloo.ca/~snew/PMATH464/chap11.pdf
Sources
- Course catalogue ↗2026–2027
- course_outline ↗Winter 2022
- course_website ↗Undated
- Official public PDF outline or course description. Materials and topic extracts may be partial; consult the linked source for the full list.
- Public lecture-note archive by Stephen New. Topics are the chapter headings in the posted notes; this is not a current-term syllabus. Source term/year not established.