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| HAL : hal-00608248, version 1 |
| arXiv : 1107.2288 |
| Fiche détaillée |  Récupérer au format |
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| What is the total Betti number of a random real hypersurface? |
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| Damien Gayet 1Jean-Yves Welschinger 1 |
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| (12/07/2011) |
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| 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. |
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| 1 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| Domaine | : | Mathématiques/Géométrie algébrique |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00608248, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00608248 | |
| oai:hal.archives-ouvertes.fr:hal-00608248 | |
| Contributeur : Damien Gayet | |
| Soumis le : Mardi 12 Juillet 2011, 15:36:48 | |
| Dernière modification le : Vendredi 6 Juillet 2012, 14:50:49 | |
