Description du projet
Une étude s’intéresse à la topologie des variétés lisses de dimension 4 et aux singularités des courbes et des surfaces
L’objectif principal du projet LDTSing, qui a reçu un financement du programme Actions Marie Skłodowska-Curie, est de tirer parti des techniques des variétés lisses de dimension 4 pour étudier les déformations des singularités de surface isolées. Plus précisément, le projet utilisera des invariants de la théorie de jauge et des techniques combinatoires de la théorie des treillis pour lisser les singularités de surface rationnelles. Le projet étudiera une conjecture de Kollár concernant une classe de singularités de surfaces rationnelles avec un lissage unique. Un autre objectif est d’étudier les propriétés de la sphère d’homologie rationnelle 3D, telles que la n-divisibilité et la torsion.
Objectif
The aim of the project is two-fold.
One goal is to employ techniques from smooth 4-dimensional topology in the study of deformations of isolated surface singularities. More specifically the project aims at advancing in the study of smoothings of rational surface singularities by means of gauge-theoretic invariants as well as lattice-theoretic combinatorial techniques. A conjecture of Kollar regarding a class of rational surface singularities with a unique smoothing will be considered. The conjecture has natural symplectic and topological counterparts. The plan consists in proving the topological version and investigating the extent to which this version of the problem can lead to advancements in the original conjecture.
Another primary goal is to investigate properties of the 3-dimensional rational homology sphere group, such as n-divisibility and torsion, via constructions involving rational cuspidal curves in possibly singular homology planes. In this context a first specific goal is producing examples of 3-manifolds which are either Seifert fibered spaces or obtained via Dehn surgery on an algebraic knots which are 2-divisible in the rational homology sphere group. In a similar setting it will be investigated the extent to which rational homology balls bounded by integral surgeries on torus knots can be realized algebraically.
Champ scientifique
Programme(s)
Régime de financement
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinateur
59000 Lille
France