Humboldt-Universität zu Berlin
Mathem.-Naturwissenschaftliche Fakultät
Institut für Mathematik
Sommersemester 2026
Time: Wednesday 13:15 - 14:45
Room: 3.007 John von Neumann-Haus
Humboldt Arithmetic Geometry Seminar
Seminar: Algebraic Geometry an der FU
| Time | Speaker | |
|---|---|---|
| 22.04.2026, 13:15 - 14: 45 | Federico Moretti (Stony Brook) | |
| Title: Picard bundles and degree of irrationality of jacobians | ||
| Abstract: The degree of irrationality of a projective variety is the smallest degree of a dominant rational map to projective space of the same dimension. I explain a vector-bundle approach via kernel bundles, implying that a globally generated bundle with positive top Chern class gives an immediate upper bound. I then study twists of Picard bundles and obtain that the degree of irrationality of any genus \(g\) Jacobian is at most \(2^g\). This is based on joint work with Andrés Rojas. | ||
| 28.04.2026, 15 - 16, Room: 1.013 | Daniel Huybrechts (Bonn) - COLLOQUIUM | |
| Title : Brauer groups: From number theory to (hyperkähler) geometry | ||
| Abstract: The Brauer group of a field was introduced a century ago, but it still holds many secrets. It started out as an object in number theory, with the theorem of Brauer—Hasse—Noether as a first highlight, and was later generalised by Grothendieck to a geometric setting. ln this talk, I will sketch certain aspects of the history that are relevant to recent developments in geometry and Hodge theory with a special emphasis on hyperkähler geometry. | ||
| 29.04.2026, 13:15 - 14:45 | Theodosis Alexandrou (HU Berlin) | |
| Title: A surface with representable \(CH_{0}\)-group but no universal zero-cycle | ||
| Abstract: We introduce a new obstruction to the existence of a universal 0-cycle on a smooth projective complex variety. As an application, we construct a smooth projective complex surface whose Chow group of 0-cycles is representable but which does not admit a universal 0-cycle. This provides a two-dimensional analogue of Voisin’s recent threefold counterexample to a question of Colliot-Thélène. As a further consequence, we exhibit the first example of a smooth projective threefold of Kodaira dimension zero carrying a non-torsion Hodge class of degree 4 that is not algebraic. The construction relies on the geometry of bielliptic surfaces of type 2. | ||
| 13.05.2026, 13:15 - 14:15 | Riccardo Redigolo (HU Berlin) | |
| Title: The scrollar invariants of curves mapping to a Hirzebruch surface | ||
| Abstract: A natural question to ask when studying \(k:1\) covers of the projective line is how line bundles split when pushed forward. A particularly interesting class of covers of \(\mathbb{P}^1\) is given by curves lying on scrolls or, more generally, by normalisations of curves lying on them. Moving in the direction of a recent conjecture of Vakil and Vemulapalli, in this talk I will show which tuples of integers can arise as the scrollar invariants of normalisations of nodal curves lying on Hirzebruch surfaces. | ||
| 27-29.05.2026 | From Geometry to Numbers: a celebration of women in mathematics | |
| For a listing of all talks, please visit the website. | ||
| 1-5.06.2026 | Algebraic curves: moduli and syzygies (Grand Hotel San Michele, Cetraro) | |
| For a listing of all talks, please visit the website. | ||
| 10.06.2026, 13:15 - 14:45 | Igor Makhlin (TU Berlin) | |
| Title: Gröbner degenerations vs. regular subdivisions | ||
| Abstract: Two notions, Gröbner (or initial) degenerations of algebraic varieties and regular subdivisions of point configurations, bear an obvious similarity: both depend on a real weight with this dependence governed by a polyhedral fan. Various authors have built on this observation to uncover deep connections between the two. A well known result of Sturmfels realizes a Gröbner degeneration of a toric variety as a union over the cells of the corresponding regular subdivision. More recently, works of Corey have shown that certain degenerations of Grassmannians and related varieties admit immersions into limits (or intersections) over regular matroid subdivisions. I will discuss a general framework which associates a point configuration with any embedded projective variety and extends the constructions of Sturmfels and Corey to this setting, interpreting them as naturally dual to each other. This talk is based on joint work with George Balla, Dan Corey and Victoria Schleis. | ||
| 23.06.2026, 11:15 - 12:45, Room 1.012 | Alessio Cela (Cambridge) | |
| Title: Interpolation for Rational Curves with Secants | ||
| 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. | ||
| 24.06.2026, 13:15 - 14:15, 14:30 - 15:30 | Jérémy Guéré (Grenoble) | |
| Title: Rational Cubic Fourfolds and Their Relation to K3 Surfaces | ||
| Abstract: I will first review the construction of atoms introduced by Katzarkov--Kontsevich--Pantev--Yu, introducing the necessary background from Gromov--Witten theory and specifically addressing the behavior of Hodge structures under Iritani's blow-up formula. I will also provide examples of computations and then introduce a new atomic invariant to prove the following theorem: if a smooth complex cubic fourfold is rational, then its primitive cohomology is isomorphic - as a rational Hodge structure - to the shifted middle cohomology of a projective K3 surface. | ||
| 8.07.2026, 13:15 - 14:45 | Debjit Basu (HU Berlin) | |
| Title: | ||
| Abstract: | ||