Humboldt University Berlin, Summer 2026
Time: Tuesdays 13:15 - 14:45
Venue: Room 3.007, Rudower Chaussee 25, 12489 Berlin
— See also the Algebraic Geometry Seminars at HU and FU —
| 21.04.2026 | Carlo Mazzanti (Bielefeld) |
| Title: | The Beauville-Voisin conjecture for double EPW quartics |
| Abstract: | Chow rings of hyperkähler varieties are best understood in settings where one has strong control over their geometry, such as for Fano varieties of lines on cubic fourfolds, while the picture is less complete for moduli spaces of sheaves on K3 surfaces. Double EPW quartics are moduli spaces of twisted sheaves, but also admit two other constructions: via conics in Verra fourfolds and as lagrangian degeneracy loci. In this talk, I will explain how these constructions interact and can be exploited to prove the Beauville--Voisin and Franchetta conjectures for them. |
| 16.06.2026 | Domenico Valloni (EPFL) |
| Title: | On p-torsion Brauer classes in characteristic p |
| Abstract: | In this talk, I will discuss the relationship between the p-torsion Brauer group and differential forms in characteristic p>0. As an example, this perspective describes the Brauer group of supersingular K3 surfaces via Kähler differentials. I will also explain the role of such Brauer classes in the Brauer–Manin obstruction and in questions concerning the density of global points. |
| 23.06.2026, 11:15-13:45, Room 1.012 | Alessio Cela (Cambridge) |
| Title: | Interpolation for Rational Curves with Secants |
| Abstract: | Abstract: In arbitrary characteristic, we determine the maximum number of general points through which a rational curve of degree d in projective space, subject to an additional secancy condition along a linear space. We consider the cases both where the points on the curve are prescribed and unprescribed, which amount to the determination of the normal and restricted tangent bundles of a general rational curve in a suitable blow-up of a projective space |
| 23.06.2026, 14:15-15:45, Room 3.007 | Alessio Bottini (Bonn) |
| Title: | The period-index problem for hyper-Kähler varieties |
| Abstract: | The Brauer group is a fundamental invariant of algebraic varieties and can be viewed as a higher analogue of the Picard group. Associated with any Brauer class are two invariants, the period and the index, whose relationship is the subject of the period-index conjecture. For hyper-Kähler varieties, whose geometry is governed by the second cohomology, one expects an even stronger form of this conjecture to hold. In this talk, I will present joint work with Daniel Huybrechts that provides new evidence for this expectation. After a brief introduction to the problem, I will discuss a proof of a variant of the conjecture in which the classical index is replaced by a Hodge-theoretic analogue. I will then explain how to verify the conjecture for most Brauer classes on hyper-Kähler varieties of K3n-type and OG10-type. |
| 30.06.2026 | Francesco Denisi (Saarland) |
| Title: | tba |
| Abstract: | tba |