Examination procedure
Oral exam
Prerequisites
Basic knowledge of classical algebraic geometry and commutative algebre. Having been introduced to the basic concepts of scheme theory, for example by following the course "Teoria degli Schemi" taught by Andrea Di Lorenzo and Mattia Talpo at the University of Pisa.
Recommended for fourth and fifth year students, and PhD students.
Syllabus
• Separated morphisms. Proper morphisms. Valuative criteria. Projective morphisms. Kähler differentials.
• Cohomology of quasi-coherent sheaves.
• Flat morphisms. Smooth morphisms.
• Applications to curves and surfaces.
Bibliographical references
Qing Liu, Algebraic Geometry and Arithmetic Curves, Oxford University Press
Robin Hartshorne, Algebraic Geometry, Springer–Verlag
David Mumford, The Red Book of Varieties and Schemes, Lecture Notes in Mathematics, Springer–Verlag
David Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer–Verlag
David Eisenbud, Joe Harris, Geometry of Schemes, Springer–Verlag
Ravi Vakil, The rising sea: Foundations of Algebraic Geometry, Princeton University Press