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Cremona transformations and special double structures

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Abstract

We consider Cremona Transformations on , whose base locus schemes are double Fossum-Ferrand structures supported on a smooth, irreducible positive dimensional subvariety. We show that if the codimension of the base locus is 2 or if its dimension is no greater than , then N=3 and such a transformation is a Cubo-Cubic Cremona Transformation not defined along a twisted cubic curve. We also prove that the same conclusion holds for such Cremona Transformations either assuming Hartshorne Conjecture on Complete Intersections or that they are defined by degree three homogeneous polynomials.

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, 91540–000, Porto Alegre, RS, Brasil

    Ivan Pan

  2. Departamento de Matemática, Universidade Federal de Pernambuco, Cidade Universitaria, 50670–901, Recife, PE, Brasil

    Francesco Russo

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  1. Ivan Pan
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  2. Francesco Russo
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Correspondence to Ivan Pan.

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First author partially supported by DMAT/UFPE and by CNPq/Bolsa de Produtividade em Pesquisa.

Second author partially supported by CNPQ/Bolsa de Produtividade em Pesquisa, and by PRONEX-FAPERJ/Geometria Algebrica e Algebra Comutativa.

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Pan, I., Russo, F. Cremona transformations and special double structures. manuscripta math. 117, 491–510 (2005). https://doi.org/10.1007/s00229-005-0573-2

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  • DOI: https://doi.org/10.1007/s00229-005-0573-2

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