Stat. Field Theory Course
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**Algebraic Geometry I**

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Barbara Fantechi

**CONTENTS**

Algebraic varieties: definition, affine and projective varieties,
examples. Products, fibered products. Separatedness and completeness.
Irreducibility and dimension theory. Tangent spaces and differentials.
Smoothness.
Schemes: definition, affine and projective schemes, examples. Reduced
schemes and varieties. Products and fibered products. Coherent,
locally free, invertible sheaves. Cotangent sheaf.
[Possibly] Smooth projective curves, correspondence
divisors/invertible sheaves, Serre duality, Riemann-Roch,
applications.

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