This note covers the following
topics: Functors, Isomorphic and equivalent categories, Representable functors,
Some constructions in the light of representable functors, Schemes: Definition
and basic properties, Properties of morphisms of schemes, general techniques and
This book is intended to give a
serious and reasonably complete introduction to algebraic geometry, not just for
experts in the field. Topics covered includes: Sheaves, Schemes, Morphisms of
schemes, Useful classes of morphisms of schemes, Closed embeddings and related
notions, Fibered products of schemes, and base change, Geometric properties:
Dimension and smoothness, Quasicoherent sheaves, Quasicoherent sheaves on
projective A-schemes, Differentials,Derived functors, Power series and the
Theorem on Formal Functions, Proof of Serre duality.
explains the following topics: Systems of algebraic equations, Affine algebraic
sets, Morphisms of affine algebraic varieties, Irreducible algebraic sets and
rational functions, Projective algebraic varieties, Morphisms of projective
algebraic varieties, Quasi-projective algebraic sets, The image of a projective
algebraic set, Finite regular maps, Dimension, Lines on hypersurfaces, Tangent
space, Local parameters, Projective embeddings and Riemann-Roch Theorem.
and Algebraic Geometry have classically enjoyed a fruitful interplay. The aim of
this series of lectures is to introduce recent development in this research
area. The topics involve classical algebraic varieties endowed with a rich
combinatorial structure, such as toric and tropical varieties.
These notes are for
a first graduate course on algebraic geometry. It is assumed that the students
are not familiar with algebraic geometry. Author has taken a moderate approach
emphasising both geometrical and algebraic thinking.
This book explains the following topics: Etale
Morphisms, Etale Fundamental Group, The Local Ring for the Etale Topology,
Sheaves for the Etale Topology, Direct and Inverse Images of Sheaves, Cohomology:
Definition and the Basic Properties, Cohomology of Curves, Cohomological
Dimension, Purity; the Gysin Sequence, The Proper Base Change Theorem,
Cohomology Groups with Compact Support, The Smooth Base Change Theorem, The
Comparison Theorem, The Kunneth Formula, Proof of the Weil Conjectures, The Weil
Conjectures, The Geometry of Lefschetz Pencils and Cohomology of Lefschetz
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.