Tags: #AG #todo/learning #resources #resources #projects/notes #MOC/resources

References: Algebraic Geometry

Texts

• Gathmann, Algebraic Geometry Course Notes ⭐
• Vakil, The Rising Sea
• Hartshorne, Algebraic Geometry
• Harris, Algebraic Geometry: A First Course
• Shafarevich, Basic Algebraic Geometry 1
• Mumford, The Red Book of Varieties and Schemes
• Fulton, Introduction to Toric Varieties
• Milne, Algebraic Geometry Notes
• Lazarsfeld, Positivity in Algebraic Geometry > Recommended by Haiyang for divisors
• Kollár-Mori, Birational Geometry of Algebraic Varieties > Recommended by Haiyang for very ample divisor, very big, nef divisors
• Kawamata, Introduction to the minimal model problem.

Notes

• McKernan’s UCSD lectures, graduate AG #resources/full-courses ^adb5c0
  • Quarter 1 ✅ 2022-06-03 ^856ee3
    • Lecture 1 ✅ 2022-06-02
    • Lecture 2 ✅ 2022-06-02
    • Lecture 3 ✅ 2022-06-02
    • Lecture 4 ✅ 2022-06-02
    • Lecture 5 ✅ 2022-06-02
    • Lecture 6 ✅ 2022-06-03
    • Lecture 7 ✅ 2022-06-03
    • Lecture 8 ✅ 2022-06-03
    • Lecture 9 ✅ 2022-06-03
    • Lecture 10 ✅ 2022-06-03
    • Lecture 11 ✅ 2022-06-03
    • Lecture 12 ✅ 2022-06-03
    • Lecture 13 ✅ 2022-06-03
    • Lecture 14 ✅ 2022-06-03
    • Lecture 15 ✅ 2022-06-03
    • Lecture 16 ✅ 2022-06-03
    • Lecture 17 ✅ 2022-06-03
    • Lecture 18 ✅ 2022-06-03
  • Quarter 2 ^a55fd7
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  • Quarter 3
    • Lecture 1 ^dd69c9
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• Sheaf cohomology:
  • https://metaphor.ethz.ch/x/2017/fs/401-4142-17L/ex/SheafCohomology.pdf
  • https://users.math.msu.edu/users/ruiterj2/Math/Documents/Fall%202019/Sheaf%20cohomology/Sheaf-cohomology-main.pdf>
• Reading seminar review of sheaf theory:
• Quick Review
• Short overview of a course
• Tripos Part 3, quick review: https://www.dpmms.cam.ac.uk/~pmhw/PtIIIAG2014.pdf
• Tripos Part III 2019 Course notes
• Harvard 233A 2017 Course notes
• Olsson course notes
• UW Spring 2016 Course
• MIT OCW 2009, Kedlaya
• MIT OCW 2015
• Harvard Math 281 Lecture Notes
• https://etale.site/livetex/256a.pdf
• https://dongryul-kim.github.io/harvard_notes/Math233a/Notes_Math233a.pdf

Topics

Standard topics

• 020 Varieties Definitions
• 022 Sheaves
• 030 Schemes
• 040 Divisors
• 050 Cohomology of Schemes
• 060 Toric Varieties
• 070 Curves and Surfaces

Advanced topics

• MSRI Summer School on toric varieties
• Seminar: ind-coherent sheaves
• Hartshorne on Deformation Theory
• MSRI Summer School on derived categories of coherent sheaves on algebraic varietes
• Minimal model program: https://web.math.princeton.edu/~jmoraga/Learning-Seminar-MMP #resources/videos

Stacks

• Seminar notes on stacks
• Masterclass: deformation theory, algebraic stacks

Exercises

• Ogus course https://math.berkeley.edu/~ogus/Math_256B-2017/index.html #examples/exercises
• Part III exams
• All AG Tripos exams