Tags: #AG #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 ample, very big, nef divisors

• Kawamata, Introduction to the minimal model problem.

• Eisenbud Commutative algebra with a view towards algebraic geometry for the commutative algebra we need.

  • The older book Introduction to commutative algebra by Atiyah and Macdonald is also fine.

• Grothendieck’s FGA, EGA, and SGA.

• Serre’s GAGA, English translation and FAC English translation

• Dolachev’s lectures on algebraic geometry

• Mumford’s red book

• The geometry of schemes by Eisenbud and Harris

• Vakil’s notes

• Dolgachev’s book “Classical Algebraic Geometry: a modern view” ## 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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    • Lecture 23

• 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

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
• #MMP: https://web.math.princeton.edu/~jmoraga/Learning-Seminar-MMP #resources/videos