Misha Verbitsky
Instituto Nacional de Matemática Pura e Aplicada
Geometria Algébrica I
Sala 232, Mondays, Fridays, 13:30-14:00, August-December 2018
Announce
Slides:
Lecture 1:
Hilbert Nullstellensatz
(August 13).
Lecture 2:
Hilbert Nullstellensatz and categories
(August 17).
Lecture 3:
Strong Nullstellensatz
(August 24).
Lecture 4:
Smooth manifolds
(August 27).
Lecture 5:
Noetherian rings and irreducible affine varieties
(August 31)
Lecture 6:
Representations of finite groups
(September 3).
Lecture 7:
Tensor product of R-modules
(September 10).
Lecture 8:
Tensor product of rings and fibered product
(September 14).
Lecture 9:
Finite-dimensional algebras over a field
(September 17).
Lecture 10:
Primitive element theorem
(September 21).
Lecture 11:
Normal varieties
(September 24).
Lecture 12:
Normalization
(September 28).
Lecture 13:
Nakayama's lemmma
(October 1).
Lecture 14:
Finite quotients and branched covers
(October 5).
Lecture 15:
Noether normalization lemma
(October 8).
Lecture 16:
Covering maos and Galois categories
(October 15).
Lecture 17:
Discriminant
(October 19).
Lecture 18:
Dimension
(October 22).
Lecture 19:
Projective varieties
(October 26).
Lecture 20:
Sheaves and algebraic varieties
(October 29).
Lecture 21:
Veronese map
(November 5).
Lecture 22:
Segre map and quadric hypersurfaces
(November 9).
Lecture 23:
Images of projective varieties are projective
(November 12).
Lecture 24:
Hilbert polynomial
(November 16).
Lecture 25:
Constructible sets
(November 19).
Handouts, homework:
Home assignment 1:
Zorn lemma
(August 17).
Home assignment 2:
Applications of Axiom of Choice
(August 17).
Home assignment 3:
Euclidean rings
(August 24).
Class assignment 4:
Exercises in set theory
(September 6).
Results.
Home assignment 5:
Hermitian spaces
(September 10)
Home assignment 6:
Tensor product
(September 14)
Class assignment 7:
Exercises in divisibility
(September 27)
Home assignment 8:
Representation of finite groups
(September 28)
Class assignment 9:
Exercises in divisibility (2)
(October 4)
Results.
Class assignment 10:
Regular functions and Nullstellensatz
(October 11)
Results.
Class assignment 11:
Representations of finite groups
(October 18)
Results.
Class assignment 12:
Noetherian rings
(October 25)
Results.
Class assignment 13:
Rational functions
(November 1)
Results.
Total score
for all assignments.
Miscellanea: test problems, exam, etc.
Exam problems
Personal problem sets
, obtained randomly with
this program.
Final results.
Misha Verbitsky
IMPA