Resources for graduate students


Here is a list of useful links for graduate students. Some of them are intended for those wishing to study algebraic geometry or related areas.

arxiv. The preprint arxiv. Where (most) mathematical results first appear.

MathSciNet. Comprehensive list of reviews of published mathematical papers (must be accessed via UMass network).

Mathoverflow. Answers to research level questions in mathematics.

MSRI videos. Videos of lectures at MSRI, Berkeley.

Atiyah. Advice for graduate students in math from Sir Michael Atiyah, one of the greatest mathematicians of the 20th century.

Terry Tao's blog. Includes a lot of useful advice on graduate study in mathematics and mathematical writing.

Upcoming conferences in algebraic geometry. Maintained by Ravi Vakil.

Mathjobs. Jobs in mathematics, hosted by the American Mathematical Society.

NSF. Main source of funding for research in pure mathematics.

Suggested reading in algebraic geometry

Introduction to algebraic curves, by P. Griffiths. googlebooks.
An introduction to Riemann surfaces assuming only basic complex analysis.

Principles of algebraic geometry, by P. Griffiths and J. Harris. googlebooks.
Complex algebraic geometry from the analytic viewpoint. It is packed with instructive examples. It may be best to skim the foundations in Chapter 0 and refer back as needed.

Hodge theory and complex algebraic geometry I, by C. Voisin. googlebooks.
Another treatment of the analytic approach. All the details are carefully explained here, but there are fewer examples. It is a good companion to Griffiths and Harris.

Chapters on algebraic surfaces, by M. Reid. arxiv.
Notes from an (unconventional) first graduate course taught by Miles Reid at Park City summer school, with a strong emphasis on examples.

Curves and their Jacobians, by D. Mumford, googlebooks.
Text of 4 expository lectures on Riemann surfaces by Mumford. It is a mine of information. The level varies so be prepared to skip some parts.

Introduction to commutative algebra, by M. Atiyah and I. MacDonald, googlebooks.
Classic reference on basic commutative algebra.

Algebraic geometry, by R. Hartshorne. googlebooks.
The standard text on algebraic geometry as developed by Grothendieck. This approach is more technical but is necessary for arithmetic applications.

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This page is maintained by Paul Hacking hacking@math.umass.edu