Hartshorne's book **Algebraic Geometry** is a classic,
covering algebraic geometry via
the theory of schemes. Students who are well-versed in this book, with their knowledge
supplemented by examples from classical algebraic geometry, are generally
ready to begin
research with me in algebraic geometry. Many of the important ideas in the book are contained
in the exercises. I encourage all students interested in mastering algebraic
geometry to try to do *all* of the exercises (but be warned that some
exercises are unsolved problems).
Forming study groups and working together is an efficient way to do this.
Students will do best with this book if they already have facility with
commutative algebra.
Hartshorne is usually used for Math 512, Modern Algebraic Geometry, at least
when I teach it. Some students have told me that they prefer Ravi Vakil's notes

A good and more introductory book is
Shafarevich, **Basic Algebraic Geometry**. The first part of the book
provides an introduction
to classical algebraic geometry (with no schemes) and contains many beautiful
examples of classical constructions. I use this book when I
teach Math 511, Introduction to Algebraic Geometry, which is offered as
a comps course every spring.

Another good introductory book is
Miranda's **Algebraic Curves and Riemann Surfaces**. This is algebraic
geometry over the complex numbers, in complex dimension 1, from both the algebraic
and transcendental points of view. I use this book
when I teach Math 510, Riemann Surfaces and Algebraic Curves, which is
offered as a comps course every fall.

Griffiths and Harris, **Principles of Algebraic Geometry**,
covers complex manifolds and algebraic geometry over the complex numbers.
Math 514, Complex Algebraic Geometry is taught every two years, next
in Fall 2018. I usually use Griffiths and Harris when I teach the
course but I sometimes use Claire Voisin's Hodge Theory book.

In addition to the core curriculum, reading courses in algebraic geometry are often offered. You are encouraged to take advantage of the opportunities presented by these (typically) advanced courses whenever you have the background.

Reading Griffiths and Harris, and Shafarevich (or taking the appropriate courses), supplemented by facility with the language of schemes (either from e.g. Hartshorne or later chapters of Shafarevich) will prepare students for doing research with me. I didn't include Miranda on this list only because Griffiths and Harris contains many of the ideas from Miranda; but reading Miranda's book could help many students prepare to study Griffiths and Harris.

- Martha Waggoner 1994, Simpson College
- Thomas Zerger 1996, Saginaw Valley State University
- Artur Elezi 1999, American University
- Mutaz Al-Sabbagh 2002, University of Damman, Saudi Arabia
- Jonathan Cox 2004, SUNY Fredonia
- Xinyun Zhu 2005, University of Texas, Permian Basin
- Joshua Mullet 2006 (co-advised with Dan Grayson), Ohio National Financial Services
- Josh Guffin 2008, Energy Solutions Forum Inc.
- Mehmet Sahin 2009
- Yong Fu 2010
- Artan Sheshmani 2011 (co-advised with Tom Nevins), Centre for Quantum Geometry of Moduli Spaces, Aarhus University, Denmark
- Jinwon Choi 2012, Sookmyung Women's University, Korea