
Course unit
ALGEBRAIC GEOMETRY 1
SC02119737, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/03 
Geometry 
8.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
4.0 
32 
68.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
Start of activities 
25/02/2019 
End of activities 
14/06/2019 
Examination board
Board 
From 
To 
Members of the board 
8 Geometria Algebrica 1  a.a. 2018/2019 
01/10/2018 
30/09/2019 
TOMMASI
ORSOLA
(Presidente)
CHIARELLOTTO
BRUNO
(Membro Effettivo)
BALDASSARRI
FRANCESCO
(Supplente)
BERTAPELLE
ALESSANDRA
(Supplente)
BOTTACIN
FRANCESCO
(Supplente)
GARUTI
MARCOANDREA
(Supplente)

Prerequisites:

Many results are based on results from commutative algebra. Basic knowledge of commutative algebra (corresponding to roughly the first half of the commutative algebra course) is recommended. 
Target skills and knowledge:

Knowledge of the basic concepts, constructions and techniques of algebraic geometry. Competence in relating the different properties of algebraic varieties and the main theoretical results about them. Problem solving skills in algebraic geometry. 
Examination methods:

Written exam. 
Assessment criteria:

Mastering the key techniques and concepts of algebric geometry.
Competence in applying the theoretical results on algebraic varieties and their properties in specific examples, for instance in the solution of exercises.
Problem solving skills in algebraic geometry. 
Course unit contents:

This course is intended as a foundational course in algebraic geometry, starting from the basics of the subject and progressing to more avanced techniques such as the study of sheaves and schemes.
Contents:
Affine varieties.
The Zariski topology.
The sheaf of regular functions on a variety.
Morphisms of varieties.
Projective varieties.
Dimension of a variety.
Introduction to schemes. 
Planned learning activities and teaching methods:

Lectures. Homework, in the form of weekly exercise sheets. The weekly exercise sheets are discussed during problem sessions. 
Additional notes about suggested reading:

The course is based on Andreas Gathmann's lecture notes at TU Kaiserslautern, available online at
http://www.mathematik.unikl.de/agag/mitglieder/professoren/gathmann/notes/alggeom/
There are weekly exercise sheets available on the Moodle page of the course. 
Textbooks (and optional supplementary readings) 

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem based learning
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Latex
 Singular (copmuter algebra software)
Sustainable Development Goals (SDGs)

