MA 6260: Algebraic Geometry I

### Pre-requisites:

Rings, Modules, Field theory.

### Class timings:

Monday: 12:00 noon to 12:50 pm

Tuesday: 09:00 am to 10:00 am

Friday: 11:00 am to 12:00 noon
### Classroom:

C-LH9 (1-4 segment); B-114 (5-6 segment)

### Examination and Grades:

The grades will be decided by the marks obtained in the assignments, mid-term, surprise tests, the final examination, and also by the performance in the class.

## Syllabus:

- Affine spaces, Projective spaces, Affine and projective varieties, The Zariski Topology, coordinate rings,
- Rational maps and Morphisms of Varieties, Local ring of a point, Products and Graphs, Algebraic Function Fields, and Dimension of Varieties, Zariski's main theorem.
- Resolution of Singularities: Rational Maps of Curves, Blowing up a Point in A^2, Blowing up Points in P^2, Quadratic Transformations, Nonsingular Models of Curves
- Riemann-Roch Theorem: Divisors, The Vector Spaces L(D), Riemann's Theorem, Derivations and Differentials, Canonical Divisors, Riemann-Roch Theorem

## References:

- Fulton, William. Algebraic curves. Mathematics Lecture Note Series. W. A. Benjamin, Inc., New York-Amsterdam, 1969.
- Musili, C. Algebraic geometry for beginners. Texts and Readings in Mathematics, 20. Hindustan Book Agency, New Delhi, 2001.
- Shafarevich, Igor R. Basic algebraic geometry. 1. Varieties in projective space. Third edition. Translated from the 2007 third Russian edition. Springer, Heidelberg, 2013.
- Steven Galbraith: Mathematics of Public Key cryptography, Cambridge University Press.

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