I am a graduate student in differential geometry and would like to learn more about algebraic geometry recently. Are there any recommended textbook/reference/lecture notes which is easier for a differential geometer to approach? Or are there any standard textbooks that can build my way up to algebraic geometry instead of some AG books for DG students?


My background for algebra is only an honor course I took in undergraduate which includes group, ring, field, and module.


Your help is very much appreciated!!



Algebraic geometry reference for differential geometer
I started some years ago from this lecture note: [Notes Algebraic Geometry 2 by by Karen Smith](https://www.google.com/url?sa=t&source=web&rct=j&url=https://pdfs.semanticscholar.org/de3b/129ed932f10e02004f36a2a5a9026e294102.pdf&ved=2ahUKEwihmKC0rsfrAhX4AxAIHXQuDwoQFjAAegQIARAB&usg=AOvVaw0WrJCd2Ib0fU98MAQLTKgD) which is about Sheaf theory and Schemes


You may need to read her first lecture note: [Notes Algebraic Geometry 1](https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.math.lsa.umich.edu/%7Ekesmith/631Lectures.pdf&ved=2ahUKEwibyYDurcfrAhU1i8MKHSOWBJcQFjAAegQIARAB&usg=AOvVaw3DX3uyAVcIxhs4pQizO2rk) which is nessesary for her second lecture note. With these two lecture notes you spend much less Time to cover all the nessesary concepts instead to read a Book.


The Book of J. P. Demailly : [Analytic methods in algebraic Geometry](https://www.google.com/url?sa=t&source=web&rct=j&url=https://www-fourier.ujf-grenoble.fr/%7Edemailly/manuscripts/analmeth.pdf&ved=2ahUKEwjz_Mb-sMfrAhXGlIsKHWA-CSIQFjAIegQIBRAB&usg=AOvVaw0hWtyQ26Mr7rb-E2SZ2AgL)  is also useful


If you are interested in Complex Geometry and Kähler Geometry , I read this Book when I was a master student ; Lectures on Kähler Manifolds - Werner Ballmann
And also
Canonical Metrics in Kähler Geometry
, Gang Tian


Also this Book is useful
Complex Geometry, Daniel Huybrechts


The Book of Hodge Theory and Complex Algebraic Geometry I and II of Claire Voisin also very useful. I read them some years ago.


