Institut de Mathématiques de Marseille, UMR 7373




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14 janvier 2019: 1 événement

Séminaire

  • Séminaire Géométrie, Dynamique et Topologie (GDT)

    Lundi 14 janvier 14:00-15:00 - Brendan OWENS - Glasgow University

    Equivariant embeddings of rational homology balls

    Résumé : I will describe a family of smooth rational homology 4-balls B_p,q, bounded by lens spaces ; these are the Milnor fibres of Wahl singularities. Smooth embeddings of B_p,q in other 4-manifolds arise in several contexts, for example in smoothings of singular projective varieties or in the rational blowdown surgery of Fintushel-Stern and J. Park. Khodorovskiy used Kirby calculus to give existence theorems for such embeddings, and these were generalised by Park-Park-Shin using methods from the minimal model program for algebraic 3-folds. Evans-Smith gave a beautiful result showing that the symplectic embeddings of B_p,q in the complex projective plane correspond to solutions of the Markov equation ; this coincides precisely with a classification by Hacking-Prokhorov of projective surfaces with quotient singularities which admit a CP^2 smoothing.
    I will describe a method for embedding B_p,q by taking double branched covers of surfaces in the 4-ball. This recovers the results of Khodorovskiy and Park-Park-Shin and also gives some interesting new embeddings. In particular we find that there are more smooth embeddings in CP^2 than those of Hacking-Prokhorov and Evans-Smith.

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