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Algebraic Combinatorics

A.Y. 2024/2025
6
Max ECTS
42
Overall hours
SSD
MAT/02
Language
Italian
Learning objectives
The course gives an introduction to Combinatorial Commutative Algebra.
Expected learning outcomes
Knowledge of the basic notions and techniques of Combinatorial Commutative Algebra.

Lesson period: First semester

Lessons timetable

Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi

Exams calendar

Single course

This course can be attended as a single course.

Take a single course
Course syllabus and organization

Single session

Responsible
Venerucci Rodolfo
Lesson period
First semester
Course syllabus
Noehterian rings and Hilbert's Basis Theorem.
Monomial ideals, monomial orders and Gröbner bases.
Free resolutions of finitely generated modules over polynomial rings and Hilbert's Syzygy Theorem.
Hilbert series of graded modules.
Simplicity complexes and Stanley-Reisner rings.
Simplicial homology and Betti numbers of monomial ideals. Hochster's formula.
Alexander duality.
Generic inizial ideals and Borel-fixed ideals.
Prerequisites for admission
Basic knowledge of Algebra (Algebra 1 and Algebra 2).
Teaching methods
Blackboard lectures.
Teaching Resources
David Eisenbud: Commutative Algebra (with a View Toward Algebraic Geometry).

David A. Cox, John Little, Donald O'Shea: Ideals, Varieties, and Algorithms (An Introduction to Computational Algebraic Geometry and Commutative Algebra).

Ezra Miller, Bernd Sturmfels: Combinatorial Commutative Algebra.

Jürgen Herzog , Takayuki Hibi: Monomial Ideals.
Assessment methods and Criteria
The final examination consists of a written exam and an oral discussion, to be given in the same session. It is not allowed to use notes, books or calculators.
MAT/02 - ALGEBRA - University credits: 6
Lessons: 42 hours
Professor: Venerucci Rodolfo
Shifts:
Turno
Professor: Venerucci Rodolfo
Professor(s)