What is the total Betti number of a random real hypersurface?
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چکیده
We bound from above the expected total Betti number of a high degree random real hypersurface in a smooth real projective manifold. This upper bound is deduced from the equirepartition of critical points of a real Lefschetz pencil restricted to the complex domain of such a random hypersurface, equirepartition which we first establish. Our proofs involve Hörmander’s theory of peak sections as well as the formula of Poincaré-Martinelli. Mathematics subject classification 2010: 14P25, 32U40, 60F10
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تاریخ انتشار 2017