Algebraic geometry can be a daunting subject to master. In this page, we collect basic textbooks that will ease you into the subject. We recommend taking the qualifying exams as early as possible. After basic courses in algebra and complex analysis, you should start reading commutative algebra and basic algebraic geometry. By the end of your first year, you should start studying the standard introductions by Hartshorne and Griffiths and Harris. You can supplement these by studying curves and surfaces or other basic topics such as intersection theory or Hodge theory. By the end of your second year, you should be mastering more advanced topics such as moduli spaces, derived categories and birational geometry.
It is extremely important to find an advisor early in graduate school. We recommend talking to several faculty members in your first year. By the end of your first year and certainly no later than the middle of your second year, you should form a working relationship with a faculty member who will be your advisor. Taking reading courses and attending research seminars are also good ways of finding an advisor.

### ** Introductory Texts in Algebraic Geometry: **

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- J. Harris, Algebraic Geometry: A First Course
- I. Shafarevich, Algebraic Geometry
- R. Hartshorne, Algebraic Geometry
- P. Griffiths and J. Harris, Principles of Algebraic Geometry
- D. Mumford, The Red Book

### ** Introductory texts in commutative algebra:**

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- M. Atiyah and I.G. MacDonald, Commutative algebra
- D. Eisenbud, Commutative algebra with a view towards algebraic geometry
- H. Matsumura, Commutative algebra

### **Books on curves:**

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- F. Kirwan, Complex algebraic curves
- R. Miranda, Algebraic curves and Riemann surfaces
- H. Farkas and I. Kra, Riemann surfaces
- E. Arbarello, M. Cornalba, P. Griffiths and J. Harris, Geometry of algebraic curves

### **Books on surfaces:**

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- A. Beauville, Complex algebraic surfaces
- W. Barth, C. Peters and A. Van de Ven, Compact complex surfaces
- D. Mumford, Curves on surfaces

### **Books on Moduli Spaces:**

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- J. Harris and I. Morrison, Moduli of Curves
- D. Mumford, Geometric Invariant Theory
- Le Potier, Lectures on vector bundles
- D. Huybrechts and M. Lehn, The geometry of the moduli spaces of sheaves

### **Books on Birational Geometry:**

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- R. Lazarsfeld, Positivity in algebraic geometry
- J. Kollar and S. Mori, Birational geometry of algebraic varieties
- J. Kollar, Rational curves on algebraic varieties

### **Books on Derived Categories:**

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- D. Huybrechts, Fourier-Mukai transforms in algebraic geometry
- S. Gelfand and Y. Manin, Methods of homological algebra

### ** Other foundational books:**

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- D. Eisenbud and J. Harris, 3264 and all that, intersection theory
- C. Voisin, Hodge theory and complex algebraic geometry
- D. Mumford, Abelian varieties