Nous obtenons une classification des feuilletages holomorphes de codimension dans dont l’application de Gauss est dégénérée.
We obtain a classification of codimension one holomorphic foliations on with degenerate Gauss maps.
Keywords: Gauss Map, Degenerate, Holomorphic Foliations
Mot clés : application de Gauss, dégénéré, feuilletages holomorphes.
@article{AIF_2010__60_2_455_0, author = {Fassarella, Thiago}, title = {Foliations with {Degenerate} {Gauss} maps on $\mathbb{P}^4$}, journal = {Annales de l'Institut Fourier}, pages = {455--487}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {2}, year = {2010}, doi = {10.5802/aif.2529}, zbl = {1192.37067}, mrnumber = {2667783}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2529/} }
TY - JOUR AU - Fassarella, Thiago TI - Foliations with Degenerate Gauss maps on $\mathbb{P}^4$ JO - Annales de l'Institut Fourier PY - 2010 SP - 455 EP - 487 VL - 60 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2529/ DO - 10.5802/aif.2529 LA - en ID - AIF_2010__60_2_455_0 ER -
%0 Journal Article %A Fassarella, Thiago %T Foliations with Degenerate Gauss maps on $\mathbb{P}^4$ %J Annales de l'Institut Fourier %D 2010 %P 455-487 %V 60 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2529/ %R 10.5802/aif.2529 %G en %F AIF_2010__60_2_455_0
Fassarella, Thiago. Foliations with Degenerate Gauss maps on $\mathbb{P}^4$. Annales de l'Institut Fourier, Tome 60 (2010) no. 2, pp. 455-487. doi : 10.5802/aif.2529. http://www.numdam.org/articles/10.5802/aif.2529/
[1] Joins and Higher secant varieties, Math. Scand., Volume 61 (1987), pp. 213-222 | MR | Zbl
[2] Differential geometry of varieties with degenerate Gauss maps, Springer, 2004 | MR
[3] Birational geometry of foliations, Monografias de Matemática. [Mathematical Monographs], Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2000 | MR | Zbl
[4] Irreducible Components of the Space of Holomorphic Foliations of Degree Two in CP(n), n 3, The Annals of Mathematics, Volume 143 (1996) no. 3, pp. 577-612 | DOI | MR | Zbl
[5] Algebraic Reduction Theorem for complex codimension one singular foliations, Comment. Math. Helv., Volume 81 (2006) no. 1, pp. 157-169 | DOI | MR | Zbl
[6] Feuilletages en droites, équations des eikonales et aures équations différentielles (2005) (arXiv:math.DS/0505601v1) | MR
[7] Terracini’s lemma and the secant variety of a curve, Proc. London Math. Soc., Volume 3 (1984), pp. 329-339 | DOI | MR | Zbl
[8] On first order congruences of lines of with a fundamental curve, manuscripta mathematica, Volume 106 (2001) no. 1, pp. 101-116 | DOI | MR | Zbl
[9] Congruences of lines with one-dimensional focal locus, Portugaliae Mathematica, Volume 61 (2004) no. 3, pp. 329-338 | MR | Zbl
[10] On first order congruences of lines in with irreducible fundamental surface, Mathematische Nachrichten, Volume 278 (2005) no. 4, pp. 363-378 | DOI | MR | Zbl
[11] On First Order Congruences of Lines in with Generically Non-reduced Fundamental Surface, Asian Journal of Mathematics, Volume 12 (2008), pp. 56-64 | MR | Zbl
[12] On the degree of polar transformations. An approach through logarithmic foliations, Selecta Mathematica, New Series, Volume 13 (2007) no. 2, pp. 239-252 | DOI | MR
[13] Ruled varieties: an introduction to algebraic differential geometry, Vieweg Verlag, 2001 | MR | Zbl
[14] Algebraic geometry and local differential geometry, Ann. Sci. Ecole Norm. Sup.(4), Volume 12 (1979) no. 3, pp. 355-452 | Numdam | MR | Zbl
[15] Cartan for beginners: differential geometry via moving frames and exterior differential systems, American Mathematical Society, 2003 | MR | Zbl
[16] Equations de Pfaff algebriques, in Lectures Notes in Mathematics, 708, 1979 | MR | Zbl
[17] Über die algebraischen Strahlensysteme, insbesondere über die der ersten und zweiten Ordnung, Abh. K. Preuss. Akad. Wiss. Berlin (1866), pp. 1-120 (also in EE Kummer, Collected Papers, Springer Verlag, 1975)
[18] Sopra i complessi d ordine uno dell , Atti Accad, Gioenia, Serie V, Catania, Volume 3 (1909), pp. 1-15 | Zbl
[19] Sui complessi di rette del primo ordine dello spazio a quattro dimensioni, Rend. Circ. Mat. Palermo, Volume 28 (1909), pp. 353-399 | DOI
[20] A tour through some classical theorems on algebraic surfaces, An. Stiint. Univ. Ovidius Constanta Ser. Mat, Volume 5 (1997), pp. 51-78 | MR | Zbl
[21] On projective varieties of dimension covered by -spaces, Illinois J.Math., Volume 46 (2002) no. 2, pp. 443-465 | MR | Zbl
[22] Completely reducible hypersurfaces in a pencil, Advances in Mathematics, Volume 219 (2008) no. 2, pp. 672-688 | DOI | MR | Zbl
[23] Surfaces of order 1 in Grassmannians, J. reine angew. Math, Volume 368 (1986), pp. 119-126 | DOI | MR | Zbl
[24] Classification of Bertini’s series of varieties of dimension less than or equal to four, Geometriae Dedicata, Volume 64 (1997) no. 2, pp. 157-191 | DOI | MR | Zbl
[25] Su una classe di superficie degl’iperspazii legate colle equazioni lineari alle derivate parziali di 2 ordine, Atti della R. Accademia delle Scienze di Torino, Volume 42 (1906), pp. 559-591
[26] Preliminari di una teoria delle varieta luoghi di spazi, Rendiconti del Circolo Matematico di Palermo, Volume 30 (1910) no. 1, pp. 87-121 | DOI
[27] Le superficie degli iperspazi con una doppia infinita di curve piane o spaziali, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur, Volume 56 (1920), pp. 75-89
[28] Sulle per cui la varieta degli –seganti ha dimensione minore dell’ ordinario, Rend. Circ. Mat. Palermo, Volume 31 (1911), pp. 392-396 | DOI
[29] Tangents and secants of algebraic varieties, Translations of mathematical monographs, 127, American Mathematical Society, Providence, R.I, 1993 | MR | Zbl
Cité par Sources :