Arthur Renaudineau (Université de Lille): Around Viro's conjecture

Abstract:  Viro's conjecture states that the first Betti number of the real part of a non-singular projective real algebraic surface is smaller than the (1,1)-Hodge number of the complexification. The first counterexample to this conjecture was constructed by Itenberg using so-called combinatorial patchworking. It opened the way to various construction of real algebraic surfaces with big Betti numbers (in small degrees and asymptotically). In this talk, I will present some of these constructions.
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