The blow-up of the projective plane at a point
The objective of the course is to introduce Mori theory, a fundamental tool in birational geometry, and the Minimal Model Program (MMP). We first treat the smooth setting, giving some proofs and examples; we then introduce the classes of singularities arising in the MMP and state the main results in greater generality.
Schedule
Venue: SISSA - room 134, on Thursday's at 14-16
19 November 2026
26 November 2026
Monday, 30 November 2026, at 11-13 (TBC)
10 December 2026
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References
R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, Springer-Verlag, New York-Heidelberg, 1977
O. Debarre, Higher-Dimensional Algebraic Geometry, Universitext, Springer-Verlag, New York, 2001 (errata corrige)
D. Eisenbud and J. Harris, The Geometry of Schemes, Graduate Texts in Mathematics, vol. 197, Springer-Verlag, New York, 2000
R. Lazarsfeld, Positivity in Algebraic Geometry I, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 48, Springer-Verlag, Berlin, 2004
R. Lazarsfeld, Positivity in Algebraic Geometry II, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 49, Springer-Verlag, Berlin, 2004