Le séminaire a lieu tous les jeudis de 13h à 14h dans la salle B217 du bâtiment des sciences.
18.9.2025
Anne Schnattinger (Neuchâtel)
Blow-ups of a quadric in P^4 along a curve yielding weak Fano threefolds
In this talk, we will examine the question of when the blow-up of a smooth quadric hypersurface in P^4 along a smooth, irreducible curve is weak Fano. We are able to give a complete answer depending only on some conditions on the geometry of the curve, particularly its degree and genus. We will introduce the notions, most importantly those of (weak) Fano threefolds, that are necessary in order to formulate the corresponding result and give the main ideas of its proof.
25.9.2025
Elias Kurz(Neuchâtel)
Birational Geometry of sexctic del pezzo surfaces
In this talk we look at non-rational del Pezzo surfaces of degree 6 and Picard rank 1 which are defined over a perfect field. We give a parametrization of their isomorphy classes and find a criteria to determine, which of them are birational to each other. We further study group homomorphisms from their group of birational transforms and give an example of a solid del Pezzo surface with infinite pliability. Joint work with Egor Yasinsky.
2.10.2025
Emelie Arvidsson (Neuchâtel)
Vanishing theorems in positive-characteristic birational geometry
I will discuss Kodaira vanishing and its generalization, the Kawamata–Viehweg vanishing theorem. Kodaira vanishing fails in general in positive characteristic, already for smooth surfaces. I will present special situations in which these theorems still hold for certain classes of surfaces, and explain how such cases can sometimes be leveraged to recover birational versions of vanishing for threefolds. I will also highlight why these results matter for the minimal model program. The talk will survey key themes in my research to date and aims to spark interest in these topics within the group.
9.10.2025
Stéphane Lamy (Toulouse)
Subgroups of plane polynomial automorphisms
I will discuss a classification of the subgroups of the group Aut(A^2) of polynomial automorphisms of the affine plane, over an arbitrary ground field. The main tool is an action of this group on a simplicial tree, coming from a structure of amalgamated product.
16.10.2025
Quentin Posva (Neuchâtel)
Moduli and singularities of varieties in positive characteristic
The aim of this talk is to introduce the audience to some challenging problems that I like, and hopefully to spark interest in some of them. I will start with a very brief review of the moduli theory of curves: this is by now a classical story, which provides a nice introduction to the moduli questions. I will also review the KSBA moduli theory, which is a successful theory for varieties of higher dimensions in characteristic 0. The main part of the talk will be about moduli questions in positive characteristic: I will explain the kinds of problems that appear, present some pathological examples one can play with, and sketch some ideas to overcome these difficulties.
20.10.2025 (lundi!)
Francesca Carroci (Roma)
Correlated GW invariants and DR cycles
In a joint work with T. Blomme we introduced a geometric refinement for log Gromov -Witten invariants of P^1-bundles on smooth projective varieties. I will introduce the correlated GW invariants and then try to explain how to compute them using a refinement of Pixton double-ramification cycle formula with target varieties. This is all joint work with T. Blomme.
23.10.2025
Paula Truöl (MPIM Bonn)
Non-complex cobordisms between quasipositive knots
Quasipositive knots occur in complex geometry as the transverse intersections of smooth algebraic curves in the complex affine plane with the 3-sphere. A complex cobordism is a surface that arises as the transverse intersection of such a smooth algebraic curve with the region bounded by two 4-balls of different radius with a common center. The two knots bounded by a complex cobordism are necessarily quasipositive, and every complex cobordism is necessarily optimal (defined in the talk). In 2016, Feller asked whether these two necessary conditions are also sufficient for the existence of a complex cobordism between two knots. In a joint work with Maciej Borodzik, we prove that they are not, for cobordisms of any genus. For genus 0, we extend our result to strongly quasipositive knots. In the talk, we will define the relevant terms and provide some context for our results.
6.11.2025
Anestis Tzogias (Neuchâtel)
Length-metric codes
We will talk about length-metric codes, a new variant of error-correcting code that we developed as an algebraic proxy for submodule codes used in physical-layer network coding, which were introduced by Gorla and Ravagnani. We will briefly summarise the history and importance of error-correcting codes in information theory, using perhaps the most well-known error-correcting codes, namely Hamming codes, as an example. We will then mention rank-metric codes and use the latter two examples to motivate some of the main problems of coding theory. Finally, we will introduce length-metric codes, which not only model submodule codes but generalise rank-metric codes. In particular, we will discuss code equivalence, optimal codes and local-to-global arguments in the length-metric. This is joint work with Elisa Gorla.
13.11.2025
Antoine Pinardin (Basel)
Cremona groups, quadric threefolds, and the icosahedron
The icosahedral group A(5) is the only non-cyclic finite simple group that occurs in the complex Cremona group in every dimension. Its actions carry substantial interest in birational geometry, and a book from Cheltsov and Shramov was dedicated to the study of its conjugacy classes in Cr(3,C). While describing them entirely is currently out of reach, a huge and more realistic step forward would be to describe all the non-linearizable actions of A(5) on minimal rational threefolds. We performed this work in the surprisingly open case of smooth quadrics, gave a full answer to the linearization problem for A(5)-actions on these varieties, and, in the non-linearizable case, gave explicitly all the minimal models to which they are equivariantly birational. I will present this project, carried out in collaboration with Zhijia Zhang.
20.11.2025
Claudia Stadlmayr (Neuchâtel)
Infinitesimal symmetry in algebraic geometry: group schemes and del Pezzo surfaces
Group schemes provide a refined notion of symmetry in positive characteristic: they detect infinitesimal structure invisible to the discrete automorphism group. Classical examples such as mu_p or alpha_p equip the trivial topological space with a non-trivial algebraic structure.
In this talk I will explain how this perspective can be used to classify weak and RDP del Pezzo surfaces admitting global vector fields, and how phenomena unique to small characteristic – such as non-lifting vector fields on rational double point singularities (RDPs) – can be illuminated using the group-scheme framework.
If time permits, I will outline applications and ongoing projects: towards higher-dimensional Fano varieties with infinite automorphism groups and (equivariant) compactifications of the affine plane.
27-28.11.2025
BENDZ SEMINAR (Basel-EPFL-Neuchâtel-Dijon-Zürich seminar in algebraic geometry)
4.12.2025
Simone Coccia (Basel)
Density of integral points on character varieties
Given a smooth complex algebraic variety Y and an algebraic group G, a (relative) G-character variety is a moduli space of G-local systems with specified behavior at the boundary of a compactification of Y. A well-known example of SL_2-character varieties are Markoff type cubic surfaces, and in recent years the study of their integral points has attracted much attention, starting with the work of Bourgain, Gamburd and Sarnak. In my talk I will present joint work with Daniel Litt where we prove that, for any algebraic variety Y, integral points are potentially Zariski dense in the relative character varieties parametrizing SL_2-local systems on Y with fixed algebraic integer traces along the boundary components. The proof first treats the case of Y a Riemann surface, where we construct one initial integral point and then produce a Zariski dense set of them by exploiting the dynamics of the mapping class group action on the character variety. The case of general Y is reduced to the Riemann surface case by using work of Corlette and Simpson.
11.12.2025
Aurore Boitrel (Aix-Marseille)
Automorphism groups of real rational Del Pezzo surfaces of degree 4
Del Pezzo surfaces and their automorphism groups play a key role in the classification up to conjugacy of subgroups of the Cremona group of the plane. Over an algebraically closed field, they are completely classified together with their automorphism groups. In this talk, we will focus on real rational Del Pezzo surfaces of degree 4. Unlike larger degrees, the degree 4 case involves an infinite moduli space of surfaces, already over the complex numbers. We will explain how studying the actions of automorphisms and of the Galois group on the conic bundle structures enables us to give a complete description of their automorphism groups by generators in terms of automorphisms and birational automorphisms.
18.12.2025
Ronan Terpereau (Lille)
tba
tba
