Algebraic Geometry I Lecture Notes Roman Bezrukavnikov
Algebraic Geometry I Lecture Notes Roman Bezrukavnikov
Algebraic Geometry I Lecture Notes Roman Bezrukavnikov
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 Quasi-coherent Sheaves, Quasi-coherent and Coherent Sheaves,
Invertible Sheaves, (Quasi)coherent sheaves on Projective Spaces, Divisors and
the Picard Group, Bezout’s Theorem, Abel-Jacobi Map, Elliptic Curves,
KSmoothness, Canonical Bundles, the Adjunction Formulaahler Differentials,
Cotangent Bundles of Grassmannians, Bertini’s Theorem, Coherent Sheves on
Curves, Derived Functors, Existence of Sheaf Cohomology, Birkhoff-Grothendieck,
Riemann-Roch, Serre Duality, Proof of Serre Duality.
This note contains the following subtopics of Algebraic Geometry,
Theory of Equations, Analytic Geometry, Affine Varieties and Hilbert’s
Nullstellensatz , Projective Varieties and Bezout’s Theorem, Epilogue
The material
presented here consists of a more or less self contained advanced course in
complex algebraic geometry presupposing only some familiarity with the theory of
algebraic curves or Riemann surfaces. But the goal, is to understand the
Enriques classification of surfaces from the point of view of Mori theory.
This is an introductory course note in algebraic geometry. Author has
trodden lightly through the theory and concentrated more on examples.Covered
topics are: Affine Geometry, Projective Geometry, The category of varieties,
Dimension theory and Differential calculus.