- Docente: Luca Battistella
- Credits: 6
- SSD: MATH-02/B
- Language: Italian
- Teaching Mode: In-person learning (entirely or partially)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 6061)
Learning outcomes
Basic affine and projective geometry.
Course contents
Projective space, coordinates, and subspaces.
Morphisms and projectivities. Projections. The group PGL(V).
Affine charts and projective closure.
Hypersurfaces, intersections with lines, singularities, flexes. Conics and quadrics. Plane cubics: classification and group law. Bézout's theorem for plane curves. Projective duality.
Linear systems: Segre, Veronese, and Cremona. Blow-up of the plane and resolution of singularities.
If time permits: Newton-Puiseux expansions, weighted projective spaces, Grassmannians.
Readings/Bibliography
- E.Sernesi, "Geometria 1", capitoli 3 e 4.
- E.Fortuna, R.Frigerio, R.Pardini, "Geometria proiettiva: problemi risolti e richiami di teoria".
Further readings:
- M.Reid, "Undergraduate algebraic geometry".
- W.Fulton, "Algebraic curves: an introduction to algebraic geometry"
- J.Harris, "Algebraic geometry: a first course".
Teaching methods
In-person lectures and exercise sessions.
Assessment methods
Oral exam including discussion of exercises (similar to the ones) assigned during the course.
Teaching tools
Teaching materials will be published on Virtuale.
Office hours
See the website of Luca Battistella