---
aliases:
- Algebraic geometry basics
- algebraic geometry
- AG
sort: 001
title: "References: Algebraic Geometry"
---

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

# References: Algebraic Geometry

## Texts

-   Gathmann, [Algebraic Geometry Course Notes](https://www.mathematik.uni-kl.de/~gathmann/de/alggeom.php) ⭐

-   Vakil, *[The Rising Sea](http://math.stanford.edu/~vakil/216blog/FOAGnov1817public.pdf)*

-   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](https://www.jmilne.org/math/CourseNotes/AG510.pdf)

-   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](attachments/Kawamata%20Intro%20MMP.pdf).

-   Eisenbud [Commutative algebra with a view towards algebraic geometry](http://books.google.com/books?isbn=0387942696) for the commutative algebra we need.

    -   The older book [Introduction to commutative algebra](http://books.google.com/books?isbn=0201407515) by Atiyah and Macdonald is also fine.

-   Grothendieck's [FGA](http://www.math.jussieu.fr/~leila/grothendieckcircle/FGA.pdf), [EGA](http://en.wikipedia.org/wiki/Elements%20de%20geometrie%20algebrique), and [SGA](http://modular.fas.harvard.edu/sga/sga/).

-   Serre's [GAGA](http://www.numdam.org/item?id=AIF_1956__6__1_0), [English translation](http://www.math.mcmaster.ca/~arnoldt/Serre-GAGA.dvi) and [FAC](http://www.jstor.org/stable/1969915) [English translation](http://students.mimuw.edu.pl/~pta/fac/fac.pdf)

-   [Dolachev's lectures on algebraic geometry](http://www.math.lsa.umich.edu/~idolga/lecturenotes.html)

-   [Mumford's red book](http://dx.doi.org/10.1007/b62130)

-   [The geometry of schemes](http://dx.doi.org/10.1007/b97680) by Eisenbud and Harris

-   [Vakil's notes](http://math.stanford.edu/~vakil/0910-216/)

-   [Dolgachev's book "Classical Algebraic Geometry: a modern view"](http://www.math.lsa.umich.edu/~idolga/CAG.pdf) 

## Notes

-   [ ] McKernan's UCSD lectures, graduate AG #resources/full-courses \^adb5c0

    -   [x] Quarter 1 ✅ 2022-06-03 \^856ee3
        -   [x] [Lecture 1](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_1.pdf) ✅ 2022-06-02
        -   [x] [Lecture 2](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_2.pdf) ✅ 2022-06-02
        -   [x] [Lecture 3](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_3.pdf) ✅ 2022-06-02
        -   [x] [Lecture 4](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_4.pdf) ✅ 2022-06-02
        -   [x] [Lecture 5](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_5.pdf) ✅ 2022-06-02
        -   [x] [Lecture 6](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_6.pdf) ✅ 2022-06-03
        -   [x] [Lecture 7](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_7.pdf) ✅ 2022-06-03
        -   [x] [Lecture 8](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_8.pdf) ✅ 2022-06-03
        -   [x] [Lecture 9](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_9.pdf) ✅ 2022-06-03
        -   [x] [Lecture 10](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_10.pdf) ✅ 2022-06-03
        -   [x] [Lecture 11](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_11.pdf) ✅ 2022-06-03
        -   [x] [Lecture 12](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_12.pdf) ✅ 2022-06-03
        -   [x] [Lecture 13](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_13.pdf) ✅ 2022-06-03
        -   [x] [Lecture 14](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_14.pdf) ✅ 2022-06-03
        -   [x] [Lecture 15](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_15.pdf) ✅ 2022-06-03
        -   [x] [Lecture 16](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_16.pdf) ✅ 2022-06-03
        -   [x] [Lecture 17](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_17.pdf) ✅ 2022-06-03
        -   [x] [Lecture 18](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Autumn/203A/l_18.pdf) ✅ 2022-06-03
    -   [ ] Quarter 2 \^a55fd7
        - [x] [Lecture 1](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_1.pdf) ✅ 2022-10-27
        - [x] [Lecture 2](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_2.pdf) ✅ 2022-10-27
        -   [ ] [Lecture 3](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_3.pdf)\
        -   [ ] [Lecture 4](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_4.pdf)\
        -   [ ] [Lecture 5](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_5.pdf)\
        -   [ ] [Lecture 6](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_6.pdf)\
        -   [ ] [Lecture 7](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_7.pdf)\
        -   [ ] [Lecture 8](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_8.pdf)\
        -   [ ] [Lecture 9](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_9.pdf)\
        -   [ ] [Lecture 10](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_10.pdf)\
        -   [ ] [Lecture 11](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_11.pdf)\
        -   [ ] [Lecture 12](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_12.pdf)\
        -   [ ] [Lecture 13](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_13.pdf)\
        -   [ ] [Lecture 14](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_14.pdf)\
        -   [ ] [Lecture 15](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_15.pdf)\
        -   [ ] [Lecture 16](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Winter/203B/l_16.pdf)
    -   [ ] Quarter 3
        -   [ ] [Lecture 1](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_1.pdf) \^dd69c9
        -   [ ] [Lecture 2](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_2.pdf)\
        -   [ ] [Lecture 3](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_3.pdf)\
        -   [ ] [Lecture 4](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_4.pdf)\
        -   [ ] [Lecture 5](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_5.pdf)\
        -   [ ] [Lecture 6](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_6.pdf)\
        -   [ ] [Lecture 7](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_7.pdf)\
        -   [ ] [Lecture 8](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_8.pdf)\
        -   [ ] [Lecture 9](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_9.pdf)\
        -   [ ] [Lecture 10](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_10.pdf)\
        -   [ ] [Lecture 11](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_11.pdf)\
        -   [ ] [Lecture 12](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_12.pdf)\
        -   [ ] [Lecture 13](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_13.pdf)\
        -   [ ] [Lecture 14](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_14.pdf)\
        -   [ ] [Lecture 15](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_15.pdf)\
        -   [ ] [Lecture 16](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_16.pdf)\
        -   [ ] [Lecture 17](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_17.pdf)\
        -   [ ] [Lecture 18](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_18.pdf)\
        -   [ ] [Lecture 19](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_19.pdf)\
        -   [ ] [Lecture 20](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_20.pdf)\
        -   [ ] [Lecture 21](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_21.pdf)\
        -   [ ] [Lecture 22](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_22.pdf)\
        -   [ ] [Lecture 23](https://mathweb.ucsd.edu/~jmckerna/Teaching/13-14/Spring/203C/l_23.pdf)

-   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:](http://www.math.toronto.edu/jkamnitz/seminar/perverse/stefan.pdf)

-   [Quick Review](http://www.mat.uniroma2.it/~ricerca/geomet/workshops/Zaidenbergnotes.pdf)

-   [Short overview of a course](attachments/2013SP_algebra.pdf)

-   Tripos Part 3, quick review: <https://www.dpmms.cam.ac.uk/~pmhw/PtIIIAG2014.pdf>

-   [Tripos Part III 2019 Course notes](http://qk206.user.srcf.net/notes/algebraic_geometry_iii.pdf)

-   [Harvard 233A 2017 Course notes](https://dongryul-kim.github.io/harvard_notes/Math233a/Notes_Math233a.pdf)

-   [Olsson course notes](https://etale.site/livetex/256a.pdf)

-   [UW Spring 2016 Course](attachments/iag.pdf)

-   [MIT OCW 2009, Kedlaya](https://ocw.mit.edu/courses/mathematics/18-726-algebraic-geometry-spring-2009/lecture-notes/)

-   [MIT OCW 2015](https://ocw.mit.edu/courses/mathematics/18-725-algebraic-geometry-fall-2015/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](https://www.msri.org/summer_schools/455)
-   [Seminar: ind-coherent sheaves](http://people.math.harvard.edu/~yifei/indcoh.html)
-   [Hartshorne on Deformation Theory](https://math.berkeley.edu/~robin/math274root.pdf)
-   [MSRI Summer School on derived categories of coherent sheaves on algebraic varietes](https://www.msri.org/summer_schools/821)
-   #MMP: <https://web.math.princeton.edu/~jmoraga/Learning-Seminar-MMP> #resources/videos