- Docente: Antonella Grassi
- Credits: 6
- SSD: MAT/03
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
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Corso:
First cycle degree programme (L) in
Mathematics (cod. 8010)
Also valid for Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Sep 20, 2023 to Dec 20, 2023
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
Other materials and papers posted on Virtuale
Teaching methods
Blackboards and digital presentations.
Assessment methods
Oral Exam
Teaching tools
Available on Virtuale.
The course takes part in the University of Bologna Project of Teaching Innovation
Office hours
See the website of Antonella Grassi