Mini-Workshop di Geometria Algebrica in collaborazione con il dottorato
Aula Beltrami: Wednesday, December 6, 2017
14.30-15.30 Alessandro Verra (Roma Tre): Old and new on rational cubic fourfolds: speculations and results
Abstract: The purpose of this talk is to survey and updating the State of the Art, concerning
the locus of rational cubic fourfolds in the family of all cubic hypersurfaces of the
complex projective 5-space. A special attention is payed to the initial cases of the
series of cubic fourfolds whose Fano variety of lines is the Hilbert scheme of two
points of a K3 surface polarized in degree d = 2(n^2 + n + 1). The interesting case
where d = 42 is considered more in detail and used to prove the unirationality of the
corresponding moduli space of K3 surfaces.
16.00-17.00 Gavril Farkas (Humboldt Universitaet zu Berlin): The Prym-Green Conjecture
Abstract: Following a tradition going back to Mumford, Tyurin and others, one can understand the geometry of torsion points on Jacobians of algebraic curves by studying the projective geometry of the associated paracanonical curve obtained by twisting the canonical bundle with the torsion point in question. By analogy with M. Green's Conjecture on syzygies of canonical curves, the
Prym-Green Conjecture predicts that the minimal resolution of a general paracanonical curve
of any level is natural, that is, as simple as possible. I will discuss a complete solution to this conjecture obtained in joint work with M. Kemeny.
Dipartimento di Matematica ''F. Casorati''
Università degli Studi di Pavia -
Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602