On blow-ups of the quintic del Pezzo 3-fold and varieties of power sums of quartic hypersurfaces

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We construct new subvarieties in the varieties of power sums for certain quartic hypersurfaces. This provides a generalization of Mukai's description of smooth prime Fano threefolds of genus twelve as the varieties of power sums for plane quartics. In fact, in our second paper, we show that these quartics are exactly the Scorza quartics associated to general pairs of trigonal curves and ineffective theta characteristics and this enables us to prove there the main cojecture of Dolgachev and Kanev.
This is the first part of the division of the paper arXiv:0801.1760. This is the basic part of our method

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Algebraic Geometry, 14J45 (Primary) 14N05, 14H42 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/228225

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0904.3586
 http://arxiv.org/abs/0904.3586

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