# INSTITUT DE MATHEMATIQUES DE BOURGOGNE

UMR 5584

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• ### [hal-01578348] Algebraic models of the real affine plane

29 août, par Adrien Dubouloz, Jérémy Blanc
We introduce a new invariant, the real (logarithmic)-Kodaira dimension, that allows to distinguish smooth real algebraic surfaces up to birational diffeomorphism. As an application, we construct infinite families of smooth rational real algebraic surfaces with trivial homology groups, whose (...)
• ### [hal-01573708] Morita equivalence of pointed fusion categories of small rank

22 août, par Michaël Mignard, Peter Schauenburg
We classify pointed fusion categories C(G, ω) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2 3 , 2 4 and 3 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their Frobenius-Schur indicators, their categorical Morita (...)
• ### [hal-01525384] From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters, the structure of the solutions and the case of fourth order

21 août, par Pierre Gaillard
We have already constructed solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants and wronskians of order 2N. These solutions have been called solutions of order N and they depend on 2N − 1 parameters. We construct here N-order rational solutions. We prove that (...)
• ### [hal-01573708] Morita equivalence of pointed fusion categories of small rank

11 août, par Michaël Mignard, Peter Schauenburg
We classify pointed fusion categories C(G, ω) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2 3 , 2 4 and 3 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their Frobenius-Schur indicators, their categorical Morita (...)
• ### [hal-01573376] Modular categories are not determined by their modular data

9 août, par Michaël Mignard, Peter Schauenburg
Arbitrarily many pairwise inequivalent modular categories can share the same modular data. We exhibit a family of examples that are module categories over twisted Drinfeld doubles of finite groups, and thus in particular integral modular (...)

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