The seminar takes place every Thursday from 1pm to 2pm in room B217 of the science building.
19.2.2026
Grâce Bockondas (Neuchâtel)
Triple lines and Eckard points on a cubic threefold
The variety that parametrizes the lines on a smooth cubic threefold is a smooth surface of general type known as the Fano surface. Among these lines, those of the second type are of particular interest: their locus in the associated Fano surface is an algebraic curve whose study goes back to Murre’s work in 1972. In this talk, we will investigate the role of triple lines in the geometry of this curve and explore the relationships between these lines and Eckardt points.
26.2.2026
Jefferson Baudin (EPFL)
A study of combinatorial and geometric properties of Q_p-rational singularities
A variety is said to have rational singularities if, roughly, the exceptional divisor of a resolution has no higher cohomology groups. For example, in the case of a surface singularity, this forces the exceptional divisor to be a tree of rational curves (hence the name “rational singularities”). There is another way to measure singularities, coming from the Minimal Model Program, via the notion of canonical singularities. One can therefore ask how these two notations relate, and a classical theorem of Elkik shows that in characteristic zero, a normal variety X whose canonical divisor K_X is Cartier has canonical singularities if and only if it has rational singularities.
In characteristic p > 0 however, there are nowadays counterexamples to rationality of canonical singularities from threefolds on. Nevertheless, it is known for a weaker notion called Q_p-rationality (up to dimension 4). In this talk, we will investigate under which assumptions these Q_p-rational singularities are actually canonical up to dimension 4. The proof will go through an explicit classification of the exceptional divisors that can occur and their shape (tree, cycles or even the real projective plane!). This is joint work with Zsolt Patakfalvi, Linus Rösler and Maciej Zdanowicz.
19.3.2026
Raymond Cheng (EPFL)
Unirationality of hypersurfaces via highly tangent lines
A classical result of Morin from 1942 shows that a general hypersurface in projective space is unirational once its degree is much smaller than its dimension; the construction is an inductive one based on fibering a hypersurface into lower degree ones via projection from a large linear space. In this talk, I will describe a new unirationality construction which based on taking residual points of highly tangent lines. This parameterization shows that a degree d hypersurface in projective n-space as soon as n ≥ 2^{d.2^d}, which significantly improves upon the previously best known bound n ≥ 2^{d!}. Furthermore, I will describe how this construction also shows that special families of very high degree hypersurfaces in positive characteristic are unirational.
26.3.2026
Arnaud Nerriere (Dijon)
Dynamics of random products of automorphisms of the plane
We consider the dynamics of random products of polynomial automorphisms of C^2. Holo-
morphic random dynamical systems were studied by Cantat–Dujardin and Roda in the case of compact
complex surfaces, and by Cantat–Dupont–Martin Baillon in the case of Markov surfaces.
We will explain how the study of the (birational) dynamics at infinity of the group gives rigidity results
of stationary measures.
2.4.2026
Nicola Ottolini (Roma Tor Vergata)
Singular intersections in families of split semiabelian varieties
The Zilber-Pink conjecture for a curve in a semiabelian variety $G$ predicts that, if the curve is not contained in a proper algebraic subgroup of $G$, then its intersection with the codimension 2 algebraic subgroups is a finite set. In the case where everything is defined over a number field, this has been proven by Barroero, Kühne and Schmidt, building on previous work of Habegger and Pila.
More recently, a variation of this problem has emerged, where one looks at the intersections of a curve with the codimension 1 algebraic subgroups, but one only considers those points in which such intersection is singular. In this talk, we will show that this set of intersections is also finite in the case of curves in families of abelian varieties and curves in split semiabelian varieties, generalizing
previous results form Marché-Maurin, Corvaja-Demeio-Masser-Zannier and Ulmer-Urzúa.
The result in the case of split semiabelian varieties has been obtained in a joint work with Ballini and Capuano.
16.4.2026
Chiara Meroni (ETHZ)
tba
23.4.2026
Yugang Zhang (Dijon)
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30.4.2026
BENDZ Seminar of algebraic geometry in Zürich
7.5.2026
Léo Navarro Chafloque(EPFL)
tba
21.5.2026
Charles Favre (Polytechnique)
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28.5.2026
Ivan Pan (Montevideo)
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