Literature Guide for Mathematics 536
There are many nice books on Algebraic Geometry of schemes,
often with different points of view on the subject.
The text for the course is Algebraic Geometry, by R. Hartshorne, Springer
Graduate Texts in Mathematics 52 This text and additional references will be placed
on reserve. This is a standard reference for the basic technical
material of schemes, cohomology, etc.
The following books, as well as a copy of the text, are on reserve in the
Mathematics Library in Hill Center:
- Schemes : the language of modern algebraic geometry , D. Eisenbud, J. Harris
- Ideals, varieties and algorithms, D. Cox et al
- Using Algebraic Geometry, D. Cox et al
- Commutative algebra with a view toward algebraic geometry,D. Eisenbud
The following books may also be useful:
- Principles of Algebraic Geometry, P. Griffiths and J. Harris
- This deals with the theory of complex varieties by using the topology and
differential geometry of complex manifolds
- Introduction to commutative algebra, M. F. Atiyah and I. G. MacDonald
- Basic algebraic geometry, I. R. Shafarevich
- Complex projective varieties I, D. Mumford
For the subject of toric varieties there is the nice short book of
Fulton and the survey of Danilov, as well as the book of Oda (the
books are on reserve in Hill, the paper is in a journal in the stacks)
- Introduction to Toric Varieties, William Fulton
- The geometry of toric varieties, V. I. Danilov: in: Russian Math. Surveys 33 (1978), no. 2, pp.
97--154
- Convex bodies and algebraic geometry, T. Oda
Online resources in algebraic geometry and toric varieties are
available. Here is a selection: