2017/18 (Roma Tre): Topics on Fano Manifolds.
Calendar/Diary:
- 01/03: Fano varieties in general: definition and first examples, Sketches on Enriques-Kodaira classification, Classification of delPezzo surfaces I.
- 29/03: Classification of delPezzo surfaces II: birational tools, weighted projective spaces. Blow up of the plane in 1,2 points. Blow up in 8 points as smooth hypersurface in a weighted projective space.
- 05/04: Classification of delPezzo surfaces III: Blow up of the plane in 7,6,5,4 points. Griffiths technique and Chern classes computations. Generalities on Grassmannians. del Pezzo of degree 5 as linear section of Gr(2,5).
- 10/04, Classification of delPezzo surfaces IV: delPezzo of degree 6. P2xP2 and P1xP1xP1 model. Relation with delPezzo of degree 5, Tom&Jerry. Current research topics on surfaces. Higher dimension: results of Kobayashi and Wisniewski. Fano manifolds of coindex 1 (del Pezzo manifolds).
- 26/04, Mukai manifolds: first classification and properties. Prime Fano 3-folds of genus < 6. There are no prime Fano 3F with g=11 or g>12. Beauville's viewpoint on the Mukai map (and equivalent cohomological vanishings).
- 03/05, Vanishing computation for low genus. Mukai's method of vector bundles. Gushel-Mukai (genus 6) threefold and fourfold. Period mapping properties and link with hyperkaheler geometry. Classification by representation theory methods.
- 24/05, Fano threefolds of genus 7,8,9,10,12. G_2, Symplectic and Orthogonal Grassmannian as key varieties. Bonus: link between the cubic fourfold and the genus 8 K3 surface.
This course is meant to be complementary to Sandro Verra's course on cubic hypersurfaces.
The (badly handwritten) notes are now available: (Notes-part 1) (Notes-part 2). Please feel free to email me with corrections and/or suggestions.
The exercises (compulsory for the exam) are here. The deadline for submission is Monday 11st June (this is the correct deadline, not June 4th stated in the pdf file).