Scheda programma d'esame
ELEMENTI DI GEOMETRIA ALGEBRICA
RITA PARDINI
Anno accademico2016/17
CdSMATEMATICA
Codice049AA
CFU6
PeriodoPrimo semestre
LinguaItaliano

ModuliSettoreTipoOreDocente/i
ELEMENTI DI GEOMETRIA ALGEBRICAMAT/03LEZIONI48
RITA PARDINI unimap
Programma non disponibile nella lingua selezionata
Learning outcomes
Knowledge
The student who successfully completes the course will be able to demonstrate a solid knowledge of the basics of Algebraic Geometry over an algebraically closed field, in particular: quasi-projective varieties, morphisms, birational equivalence and dimension theory.
Assessment criteria of knowledge
The student will be assessed on his/her demonstrated ability to discuss the main course contents, the knowledge of the theorems presented in the course and reproduce their proofs, using the appropriate terminology.

Methods:

  • Final oral exam

Teaching methods

Delivery: face to face

Learning activities:

  • attending lectures

Attendance: Advised

Teaching methods:

  • Lectures

Syllabus
Plane curves: local geometry, weak form Bezout's theorem. Plane cubics: the J-invariant, the group law. Nullstellensatz. Quasi-projective varieties: Zariski topology, morphisms, birational maps, dimension, tangent spaces. Segre varieties, Veronese varieties, Grassmannians.
Bibliography
Recommended reading includes parts of the following texts: 1) E. Fortuna, R. Frigerio, R. Pardini, Geometria proiettiva, Problemi risolti e richiami di teoria, UNITEXT Springer (2011). 3) M. Reid, Undergraduate Algebraic Geometry, Cambridge University Press (1988). 3) I. R. Shafarevich, Basic Algebraic Geometry 1, (Second edition), Springer (1994). Further bibliography will be indicated during the course.
Ultimo aggiornamento 14/11/2016 17:27