- Docente: Antonella Grassi
- Credits: 6
- SSD: MAT/03
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
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Corso:
Second cycle degree programme (LM) in
Mathematics (cod. 5827)
Also valid for First cycle degree programme (L) in Mathematics (cod. 8010)
Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
The goal of the course is to provide a robust introduction to techniques, problems and applications in algebraic geometry.
Course contents
Introduction to affine and projetice curves and surfaces, as abstract algebraic varieties and their properties.
Ideals, varieties, ring of functions, field of functions. Examples. Maps, Morphisms. Abstract varieties. Weighted projective spaces and other examples. Singular and non singular varities. Dimensions. Quotients. Volume forms. The canonical divisor. Adjunction formula. Divisors, linear systems. Examples and applications. Birationality problems; Rationality questions.
The courses Curves and Surfaces and Projective Geometry can be taken in the same year or in different years, in any sequence. The courses do not overlap, rather, they complement each other; the syllabi wiil be coordinated.
Readings/Bibliography
M. Reid, Undergraduate Algebraic Geometry
A. Grassi, Appunti del corso
Other materials and papers posted on Virtuale
Teaching methods
Blackboards and digital presentations.
Assessment methods
Oral exam.
Office hours
See the website of Antonella Grassi
SDGs
This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.