Course page for Algebraic Geometry I

MA 6260: Algebraic Geometry I

Pre-requisites:

Rings, Modules, Field theory.

Class timings:

Monday: XX:XX to XX:XX
Friday: XX:XX to XX:XX

Classroom:

XXXX

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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