This is a continuation course to ’Algebraic Geometry’ offered last semester. We will be covering the following topics:
• Integral extensions, normalisation and flatness from commutative algebra.
• S-valued points and the functor of points.
• Weil, Cartier divisors and line bundles.
• Kähler differentials and the cotangent bundle.
• Proper morphisms and more on the Proj construction.
• Cohomology of sheaves and Cech cohomology.
• Cohomology of projective space.
• Flatness and generic smoothness.
• Serre duality and Riemann-Roch for curves.
• Introduction to surface theory.
References: We will follow a mixture of references:
Notes by Ottem-Ellingsrud.
Hartshorne's 'Algebraic Geometry'.
Notes by Vakil.
Mumford's 'Red book of varieties and schemes'.
Görtz-Wedhorn 'Algebraic geometry 1: Schemes with examples and exercises'.