# INSTITUT DE MATHEMATIQUES DE BOURGOGNE

UMR 5584

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• ### [hal-01504996] On codimension two embeddings up to link-homotopy

31 octobre, par Benjamin Audoux, Jean-Baptiste Meilhan, Emmanuel Wagner
We consider knotted annuli in 4–space, called 2–string-links, which are knotted surfaces in codi-mension two that are naturally related, via closure operations, to both 2–links and 2–torus links. We classify 2–string-links up to link-homotopy by means of a 4–dimensional version of Milnor invariants. (...)
• ### [hal-01622447] Deformations of $\mathbb{A}^1$-cylindrical varieties

27 octobre, par Adrien Dubouloz, Takashi Kishimoto
An algebraic variety is called $\mathbbA^1$-cylindrical if it contains an $\mathbbA^1$-cylinder, i.e. a Zariski open subset of the form $Z\times\mathbbA^1$ for some algebraic variety $Z$. We show that the generic fiber of a family $f:X\rightarrow S$ of normal $\mathbbA^1$-cylindrical varieties (...)
• ### [hal-01619911] Symbolic Computations of First Integrals for Polynomial Vector Fields

23 octobre, par Guillaume Chèze, Thierry Combot
In this article we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for computing , if it exists, a rational, Darbouxian, Liouvillian or Riccati first integral with bounded degree of a (...)
• ### [hal-01620406] Automorphisms of $\mathbb{P}^1$-bundles over rational surfaces

20 octobre, par Jérémy Blanc, Andrea Fanelli, Ronan Terpereau
In this paper we provide the complete classification of $\mathbbP^1$-bundles over smooth projective rational surfaces whose neutral component of the automorphism group is maximal. Our results hold over any algebraically closed field of characteristic (...)
• ### [hal-01620368] Stability conditions and related filtrations for $(G,h)$-constellations

20 octobre, par Ronan Terpereau, Alfonso Zamora
Given an infinite reductive algebraic group $G$, we consider $G$-equivariant coherent sheaves with prescribed multiplicities, called $(G,h)$-constellations, for which two stability notions arise. The first one is analogous to the $\theta$-stability defined for quiver representations by King and (...)

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