Study programme 20232024  Français  
Algebraic Geometry Project (List A)  
Programme component of Master's in Mathematics (MONS) (day schedule) à la Faculty of Science 
Code  Type  Head of UE  Department’s contact details  Teacher(s) 

USM1SCMATH003M  Optional UE  VOLKOV Maja  S843  Géométrie algébrique 

Language of instruction  Language of assessment  HT(*)  HTPE(*)  HTPS(*)  HR(*)  HD(*)  Credits  Weighting  Term 

 Français  30  0  90  0  0  12  12.00  Full academic year 
AA Code  Teaching Activity (AA)  HT(*)  HTPE(*)  HTPS(*)  HR(*)  HD(*)  Term  Weighting 

SMATH046  Algebraic Geometry Project  30  0  90  0  0  A  100.00% 
Programme component 

Objectives of Programme's Learning Outcomes
Learning Outcomes of UE
Introduction to commutative algebra.
Introduction to affine and projective algebraic geometry.
The aim of this course is to master the correspondence between algebraic geometry and commutative algebra over an algebraically closed field.
UE Content: description and pedagogical relevance
Arithmetics of polynomial rings, modules, integrality, Noetherian rings, localisation.
Hilberts Nullstellensatz, Zariski topology, topological irreducibility, regular maps, products, rational maps, dimension, smoothness.
Projective space, projective and quasiprojective objects, morphisms.
Prior Experience
Bachelor's degree Algebra courses, elementary general toplogy.
Type of Teaching Activity/Activities
AA  Type of Teaching Activity/Activities 

SMATH046 

Mode of delivery
AA  Mode of delivery 

SMATH046 

Required Learning Resources/Tools
AA  Required Learning Resources/Tools 

SMATH046  M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra, AddisonWesley D. Perrin, Géométrie Algébrique, CNRS Editions 
Recommended Learning Resources/Tools
AA  Recommended Learning Resources/Tools 

SMATH046  S. Lang, Algebra, Graduate Texts in Mathematics 211, SpringerVerlag 
Other Recommended Reading
AA  Other Recommended Reading 

SMATH046  M. Reid, Undergraduate Algebraic Geometry, London Mathematical Society Student Texts, Cambridge University Press I.R. Shafarevich, Basic Algebraic Geometry Volume 1, SpringerVerlag 
Grade Deferrals of AAs from one year to the next
AA  Grade Deferrals of AAs from one year to the next 

SMATH046  Authorized 
Term 1 Assessment  type
AA  Type(s) and mode(s) of Q1 assessment 

SMATH046 

Term 1 Assessment  comments
AA  Term 1 Assessment  comments 

SMATH046  Continuous assessment throughout the academic year. 
Resit Assessment  Term 1 (B1BA1)  type
AA  Type(s) and mode(s) of Q1 resit assessment (BAB1) 

SMATH046 

Term 2 Assessment  type
AA  Type(s) and mode(s) of Q2 assessment 

SMATH046 

Term 2 Assessment  comments
AA  Term 2 Assessment  comments 

SMATH046  Continuous assessment throughout the academic year. 
Term 3 Assessment  type
AA  Type(s) and mode(s) of Q3 assessment 

SMATH046 

Term 3 Assessment  comments
AA  Term 3 Assessment  comments 

SMATH046  Not applicable 