Geometrie classique des feuilletages quadratiques TeX Export

@article{citeulike:4016285, abstract = {The set \$\mathscr{F}(2;2)\$ of quadratic foliations on the complex projectiveplane can be identified with a Zariski's open set of a projective space ofdimension 14 on which acts \$\mathrm{Aut}(\mathbb{P}^2(\mathbb{C})).\$ Weclassify, up to automorphisms of \$\mathbb{P}^2(\mathbb{C}),\$ quadraticfoliations with only one singularity. This allows us to describe the action of\$\mathrm{Aut}(\mathbb{P}^2(\mathbb{C}))\$ on \$\mathscr{F}(2;2).\$ On the one handwe show that the dimension of the orbits is more than 6 and that there areexactly two orbits of dimension \$6;\$ on the other hand we obtain that theclosure of the generic orbit in \$\mathscr{F}(2;2)\$ contains at least sevenorbits of dimension 7 and exactly one orbit of dimension \$6.\$}, archivePrefix = {arXiv}, author = {Cerveau, D. and Deserti, J. and Belko, Garba D. and Meziani, R.}, citeulike-article-id = {4016285}, citeulike-linkout-0 = {http://arxiv.org/abs/0902.0877}, citeulike-linkout-1 = {http://arxiv.org/pdf/0902.0877}, eprint = {0902.0877}, keywords = {foliations, integrability, polynomial\_vector\_fields, quadratic\_fields}, month = {Feb}, posted-at = {2009-02-06 14:37:08}, priority = {4}, title = {Geometrie classique des feuilletages quadratiques}, url = {http://arxiv.org/abs/0902.0877}, year = {2009} }

TY - JOUR ID - citeulike:4016285 L3 - citeulike-article-id:4016285 N2 - The set $\mathscr{F}(2;2)$ of quadratic foliations on the complex projectiveplane can be identified with a Zariski's open set of a projective space ofdimension 14 on which acts $\mathrm{Aut}(\mathbb{P}^2(\mathbb{C})).$ Weclassify, up to automorphisms of $\mathbb{P}^2(\mathbb{C}),$ quadraticfoliations with only one singularity. This allows us to describe the action of$\mathrm{Aut}(\mathbb{P}^2(\mathbb{C}))$ on $\mathscr{F}(2;2).$ On the one handwe show that the dimension of the orbits is more than 6 and that there areexactly two orbits of dimension $6;$ on the other hand we obtain that theclosure of the generic orbit in $\mathscr{F}(2;2)$ contains at least sevenorbits of dimension 7 and exactly one orbit of dimension $6.$ TI - Geometrie classique des feuilletages quadratiques KW - foliations KW - integrability KW - polynomial_vector_fields KW - quadratic_fields AU - Cerveau, D AU - Deserti, J AU - Belko, Garba AU - Meziani, R PY - 2009/Feb/05/ UR - http://arxiv.org/abs/0902.0877 ER -