Winter Semester 2018/19
Rationality of algebraic varieties with an emphasis on cubics
Each Tuesday from 09:30 (s.t.) in the BMS Seminar Room 1.023 in the HU Math Department in Adlershof.
First meeting: Tuesday, 23 October 2018.
The course aims to study rationality of algebraic varieties with am emphasis on cubic hypersurfaces from the point of view of complex projective algebraic geometry. Elementary and basic tools will be constructed to address the geometry of these varieties and some important related topics in dimension 3 and 4. Here is a list of the topics to be covered:
I. Basic algebraic geometry of cubic hypersurfaces. The polar linear system of quadrics, the Hessian, the Fano variety of lines. Special examples of cubics. Cubics with many nodes.
II. Historical perspective on rationality problems. Cubic threefolds: intermediate Jacobian. Clemens-Griffiths theory. Methods to prove irrationality. Quartic double solids: Voisin’s recent results of non stable rationality.
III. Cubic fourfolds. Examples of rational cubic fourfolds. Conjecturally rational cubic four- folds and K3 surfaces. Families of cubic fourfolds whose Fano variety of lines is the Hilbert scheme of two points of a K3. Enumerative geometry of nodal rational scrolls for special cubic fourfolds. Moduli of polarized K3 surfaces and cubic fourfolds.
Einstein Workshop Geometric and Topological Combinatorics
29-31 October 2018
Einstein Workshop on Algebraic Combinatorics
1-2 November 2018
Block seminar Geometric and Algebraic Combinatorics
29 October 2018, 2 November 2018, 16 November 2018