First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
ALGEBRAIC GEOMETRY 1
SC02119737, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2019/20
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination ALGEBRAIC GEOMETRY 1
Website of the academic structure http://matematica.scienze.unipd.it/2019/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge ORSOLA TOMMASI MAT/03

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
SC02119737 ALGEBRAIC GEOMETRY 1 ORSOLA TOMMASI SC1172

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Examination board not defined

Syllabus
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, possibly taking homework assignments into account.
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
https://www.mathematik.uni-kl.de/~gathmann/de/alggeom.php
The structure of the course will follow the 2003 version of Gathmann's notes, with some material added or substituted from the version of 2014.

There are weekly exercise sheets available on the Moodle page of the course.


Additional references:

- for the parts about affine varieties and varieties in projective space, a good complementary reference is

I. R. Shafarevich, Basic algebraic geometry. 1. Varieties in projective space. Second edition. Translated from the 1988 Russian edition and with notes by Miles Reid. Springer-Verlag, Berlin, 1994. xx+303 pp. ISBN: 3-540-54812-2

- for the part about schemes and sheaves one may refer to

I. R. Shafarevich, Basic algebraic geometry. 2.Schemes and complex manifolds. Second edition. Translated from the 1988 Russian edition and with notes by Miles Reid. Springer-Verlag, Berlin, 1994. xiv+269 pp. ISBN: 3-540-57554-5

I. G. Macdonald, Algebraic geometry. Introduction to schemes. W. A. Benjamin, Inc., New York-Amsterdam 1968 vii+113 pp.
Textbooks (and optional supplementary readings)

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Problem based learning
  • Problem solving

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • Latex

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