The nef cone of the moduli space of sheaves and strong Bogomolov inequalities |
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Authors: | Izzet Coskun Jack Huizenga |
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Affiliation: | 1.Aix-Marseille Université,CNRS, Centrale Marseille, I2M, UMR 7373,Marseille,France;2.Steklov Mathematical Institute of RAS,Moscow,Russia;3.Institute for Information Transmission Problems,Moscow,Russia;4.National Research University Higher School of Economics,Moscow,Russia;5.Department of Mathematics,Bar-Ilan University,Ramat-Gan,Israel |
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Abstract: | The paper is devoted to generic translation flows corresponding to Abelian differentials with one zero of order two on flat surfaces of genus two. These flows are weakly mixing by the Avila–Forni theorem. Our main result gives first quantitative estimates on their spectrum, establishing the Hölder property for the spectral measures of Lipschitz functions. The proof proceeds via uniform estimates of twisted Birkhoff integrals in the symbolic framework of random Markov compacta and arguments of Diophantine nature in the spirit of Salem, Erd?s and Kahane. |
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