Algebraic Geometry I Lecture Notes Roman Bezrukavnikov

Overview & Synopsis

The
contents of this book include, Course Introduction, Zariski topology, Affine
Varieties, Projective Varieties, Noether Normalization, Grassmannians, Finite
and Affine Morphisms, More on Finite Morphisms and Irreducible Varieties,
Function Field, Dominant Maps, Product of Varieties, Separateness, Sheaf
Functors and Quasicoherent Sheaves, Quasicoherent and Coherent Sheaves,
Invertible Sheaves, Quasi coherent sheaves on Projective Spaces, Divisors and
the Picard Group, Bezouts Theorem, AbelJacobi Map, Elliptic Curves,
KSmoothness, Canonical Bundles, the Adjunction Formulaahler Differentials,
Cotangent Bundles of Grassmannians, Bertinis Theorem, Coherent Sheves on
Curves, Derived Functors, Existence of Sheaf Cohomology, BirkhoffGrothendieck,
RiemannRoch, Serre Duality, Proof of Serre Duality.