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.
5.3.2026
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12.3.2026
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19.3.2026
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26.3.2026
Arnaud Nerriere (Dijon)
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2.4.2026
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16.4.2026
Chiara Meroni (ETHZ)
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23.4.2026
Yugang Zhang (Dijon)
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30.4.2026
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7.5.2026
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21.5.2026
Charles Favre (Polytechnique)
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28.5.2026
Ivan Pan (Montevideo)
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