MA6003: Introduction to Algebraic Geometry

Polynomial rings over fields, Hilbert basis theorem, Maximal ideals in polynomial rings over
algebraically closed fields and Hilbert’s Nullstellensatz, affine algebraic sets, affine algebraic varieties,
projective varieties.

Morphisms of varieties and rational maps, Local rings and germs of functions on varieties, krull
dimension of rings and dimension of varieties, Nonsingular varieties, Jacobian criterion.
Sheaves, locally ringed spaces, schemes, morphisms of schemes.

TEXTBOOKS

(a) Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics : 52, Springer,
ISBN 978-1-4419-2807-8, ISBN 978-1-4757-3849-0 (eBook)
(b) Joe Harris, Algebraic Geometry : a first course, Graduate texts in Mathematics : 133,
Springer, ISBN 978-1-4419-3099-6, ISBN 978-1-4757-2189-8(eBook).

REFERENCES

(a) Qing Liu, Algebraic Geometry and Arithmetic curves, OUP Oxford, 2006, ISBN 0-19-850284-2,
ISBN 978-0-19-850284-5.
(b) Kenji Ueno, An introduction to algebraic geometry, American Mathematical Society, ISBN
0-8218-0589-4, ISBN 978-0-8218-1144-3
(c) David Mumford, The Red Book of Varieties and Schemes, Lecture Notes in Mathematics
1358, Springer-Verlag, ISBN 978-3-540-50497-9, ISBN 978-3-662-21581-4 (eBook)