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New simply connected surfaces of general type

Ponente: Xavier Roulleau
Institución: Université de Poitiers
Tipo de Evento: Investigación
Cuándo 10/03/2016
de 13:00 a 14:00
Dónde Salon de Seminarios Graciela Salicrup
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The Chern numbers c_1^2, c_2 of a smooth minimal surface of general type X satisfy the so called Bogomolov-Miyaoka-Yau inequality: c_1^2 ≤ 3c_2. Thirty-five years ago, Bogomolov asked if one can improve the BMY inequality to c_1^2≤ a c_2 with a<3 when one moreover supposes that X is simply connected. In this talk, we show that there exists spin (resp. non-spin) simply connected surfaces with c_1^2/c_2 arbitrarily close to 3, and therefore the answer is negative. This is a joint work with Giancarlo Urzúa.